INTRODUCTION TO BUSINESS STATISTICS 7TH EDITION BY RONALD WEIERS - TEST BANK

INTRODUCTION TO BUSINESS STATISTICS 7TH EDITION BY RONALD WEIERS – TEST BANK

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Chapter 5: Probability: Review of Basic Concepts

Student: ___________________________________________________________________________

True or False
Uncertainty plays an important role in our daily lives and activities as well as in business.
True False

True or False
In the classical approach, probability is the proportion of times an event is observed to occur in a very larger number of trials.
True False

True or False
Sometimes it is useful to revise a probability on the basis of additional information that we didn’t have before.
True False

True or False
An experiment is an activity of measurement that results in an outcome.
True False

True or False
In general, an event is one of the possible outcomes of an experiment.
True False

True or False
The relative frequency approach to probability is judgmental, representing the degree to which one happens to believe that an event will or will not happen.
True False

If the probability of an event is x, with , then the odds in favor of the event are x to (1 – x).
True False

True or False
The union of events describes two or more events occurring at the same time.
True False

True or False
When the events within a set are both mutually exclusive and exhaustive, the sum of their probabilities is 1.0.
True False

True or False
When events are mutually exclusive, two or more of them can happen at the same time.
True False

True or False
If P(A) = 0.5 and P(B) = 0.80, then P(A or B) must be 0.95.
True False

True or False
When events A and B are independent, then P(A and B) = P(A) + P(B).
True False

True or False
Bayes’ theorem is an extension of the concept of conditional probability.
True False

True or False
Prior probability is a marginal probability while posterior probability is a conditional probability.
True False

If the event of interest is A, then:
A. the probability that A will not occur is [1 – P(A)].
B. the probability that A will not occur is the complement of A.
C. the probability is zero if event A is impossible.
D. the probability is one if event A is certain.
E. All of these are true.

The classical approach describes a probability:
A. in terms of the proportion of times an event is observed to occur in a very large number of trials.
B. in terms of the degree to which one happens to believe that an event will happen.
C. in terms of the proportion of times that an event can be theoretically expected to occur.
D. is dependent on the law of large numbers.
E. describes an event for which all outcomes are equally likely.

An example of the classical approach to probability would be:
A. the estimate of number of defective parts based on previous production data.
B. your estimate of the probability of a pop quiz in class on a given day.
C. the annual estimate of the number of deaths of persons age 25.
D. the probability of drawing an Ace from a deck of cards.

If a set of events includes all the possible outcomes of an experiment, these events are considered to be:
A. mutually exclusive.
B. exhaustive.
C. intersecting.
D. inclusive.
E. None of the above.

A student is randomly selected from a class. Event A = the student is a male and Event B = the student is a female. Events A and B are:
A. mutually exclusive.
B. exhaustive.
C. intersecting.
D. dependent.
E. both A and B.

Which of the following is not an approach to assigning probabilities?
A. The Classical approach
B. The Trial and error approach
C. The Relative frequency approach
D. The Subjective approach
E. All of the above are approaches to assigning probabilities.

If Events A and B are not mutually exclusive, then the probability that one of the events will occur is represented by
A. P(A or B) = P(A) + P(B) – P(A and B)
B. P(A or B) = P(A) + P(B)
C. P(A and B) = P(A) + P(B) – P(A or B)
D. P(A and B) = P(A) + P(B)
E. P(A or B) = P(A) + P(B) + P(A and B)

Which of the following statements is not correct?
A. Two events A and B are mutually exclusive if event A occurs and event B cannot occur.
B. If events A and B occur at the same time, then A and B intersect.
C. If event A does not occur, then its complement A‘ will also not occur.
D. A union of events occurs when at least one event in a group occurs, e.g., (A or B or C).
E. If all possible outcomes of an experiment are represented in a set, the set is considered exhaustive.

If a contingency table shows the sex and classification of undergraduate students (freshman, sophomore, junior, senior) in your statistics class, which of the following is true?
A. The sex of the student is an example of mutually exclusive events.
B. Because yours is an undergraduate class, the events are exhaustive, i.e., each student must fall in one of the classifications.
C. An example for the intersection of events would be the number of males who are juniors.
D. An example for the union of events would be the number of students who are female or juniors.
E. All of these are true.

The table below gives the probabilities of combinations of religion and political parties in a major U.S. city.
Which of the following represents two mutually exclusive events?
A. (A and D).
B. (A and E).
C. (A and F).
D. (A and G).
E. All of these are mutually exclusive.

The table below gives the probabilities of combinations of religion and political parties in a major U.S. city.
Which two of the following pairs of events intersect?
A. A and D
B. A and E
C. F and E
D. B and C
E. D and B

The table below gives the probabilities of combinations of religion and political parties in a major U.S. city.
What is the probability that a randomly selected person would be a Protestant and at the same time be a Democrat or a Republican?
A. 0.67
B. 0.35
C. 0.95
D. 0.89
E. 0.62

The table below gives the probabilities of combinations of religion and political parties in a major U.S. city.
What is the probability that a randomly selected person would be an independent whose religion was neither Protestant nor Catholic?
A. 0.05
B. 0.03
C. 0.02
D. 0.01

The table below gives the probabilities of combinations of religion and political parties in a major U.S. city.
What is the probability that a randomly selected person would be a Democrat who was not Jewish?
A. 0.93
B. 0.50
C. 0.47
D. 0.07
E. None of these

The table below gives the probabilities of combinations of religion and political parties in a major U.S. city.
What is the probability that a randomly selected person would be a Republican?
A. 0.67
B. 0.22
C. 0.11
D. 0.39
E. None of these

Two events A and B are said to be mutually exclusive if:
A. P (A /B) = 1.
B. P (B /A) =1.
C. P (A and B) =1.
D. P (A and B) = 0.

If P(A) = 0.84, P(B) = 0.76 and P(A or B) = 0.90, then P(A and B) is:
A. 0.06.
B. 0.14.
C. 0.70.
D. 0.83.

If P(A) = 0.25 and P(B) = 0.60, then P(A and B) is:
A. 0.15.
B. 0.35.
C. 0.85.
D. Cannot be determined from the information given.

A basketball team at a university is composed of ten players. The team is made up of players who play either guard, forward, or center position. Four of the ten are guards; four of the ten are forwards; and two of the ten are centers. The numbers of the players are 1, 2, 3, 4, for the guards; 5, 6, 7, 8 for the forwards; and 9 and 10 for the centers. The starting five are numbered 1, 3, 5, 7, and 9. Let a player be selected at random from the ten. Define the following events:

A = player selected has a number from 1 to 8.

B = player selected is a guard.

C = player selected is a forward.

D = player selected is a starter.

E = player selected is a center.

P(A) is equal to:
A. 0.80.
B. 0.40.
C. 0.50.
D. 0.20.
E. 0.60.

A basketball team at a university is composed of ten players. The team is made up of players who play either guard, forward, or center position. Four of the ten are guards; four of the ten are forwards; and two of the ten are centers. The numbers of the players are 1, 2, 3, 4, for the guards; 5, 6, 7, 8 for the forwards; and 9 and 10 for the centers. The starting five are numbered 1, 3, 5, 7, and 9. Let a player be selected at random from the ten. Define the following events:

A = player selected has a number from 1 to 8.

B = player selected is a guard.

C = player selected is a forward.

D = player selected is a starter.

E = player selected is a center.

P(B) is equal to:
A. 0.80.
B. 0.40.
C. 0.50.
D. 0.20.
E. 0.30.

A basketball team at a university is composed of ten players. The team is made up of players who play either guard, forward, or center position. Four of the ten are guards; four of the ten are forwards; and two of the ten are centers. The numbers of the players are 1, 2, 3, 4, for the guards; 5, 6, 7, 8 for the forwards; and 9 and 10 for the centers. The starting five are numbered 1, 3, 5, 7, and 9. Let a player be selected at random from the ten. Define the following events:

A = player selected has a number from 1 to 8.

B = player selected is a guard.

C = player selected is a forward.

D = player selected is a starter.

E = player selected is a center.

P(D and E) is equal to:
A. 0.10.
B. 0.05.
C. 0.50.
D. 0.20.
E. 0.60.

A basketball team at a university is composed of ten players. The team is made up of players who play either guard, forward, or center position. Four of the ten are guards; four of the ten are forwards; and two of the ten are centers. The numbers of the players are 1, 2, 3, 4, for the guards; 5, 6, 7, 8 for the forwards; and 9 and 10 for the centers. The starting five are numbered 1, 3, 5, 7, and 9. Let a player be selected at random from the ten. Define the following events:

A = player selected has a number from 1 to 8.

B = player selected is a guard.

C = player selected is a forward.

D = player selected is a starter.

E = player selected is a center.

P(B and D) is equal to:
A. 0.80.
B. 0.40.
C. 0.50.
D. 0.20.
E. 0.30.

A basketball team at a university is composed of ten players. The team is made up of players who play either guard, forward, or center position. Four of the ten are guards; four of the ten are forwards; and two of the ten are centers. The numbers of the players are 1, 2, 3, 4, for the guards; 5, 6, 7, 8 for the forwards; and 9 and 10 for the centers. The starting five are numbered 1, 3, 5, 7, and 9. Let a player be selected at random from the ten. Define the following events:

A = player selected has a number from 1 to 8.

B = player selected is a guard.

C = player selected is a forward.

D = player selected is a starter.

E = player selected is a center.

P(B /D) is equal to:
A. 0.80.
B. 0.40.
C. 0.50.
D. 0.20.
E. 0.60.

A basketball team at a university is composed of ten players. The team is made up of players who play either guard, forward, or center position. Four of the ten are guards; four of the ten are forwards; and two of the ten are centers. The numbers of the players are 1, 2, 3, 4, for the guards; 5, 6, 7, 8 for the forwards; and 9 and 10 for the centers. The starting five are numbered 1, 3, 5, 7, and 9. Let a player be selected at random from the ten. Define the following events:

A = player selected has a number from 1 to 8.

B = player selected is a guard.

C = player selected is a forward.

D = player selected is a starter.

E = player selected is a center.

P(E /D) is equal to:
A. 0.80.
B. 0.40.
C. 0.50.
D. 0.20.
E. 0.10.

A useful graphical method of constructing the sample space for an experiment is:
A. tree diagram.
B. pie chart.
C. histogram.
D. bar graph.
E. scatter plot

Assume that A and B are independent events with P(A) = 0.40 and P(B) = 0.30. The probability that both events will occur simultaneously is:
A. 0.10.
B. 0.12.
C. 0.70.
D. 0.75.
E. 1.0.

Two events A and B are said to be independent if:
A. P(A and B) = P(A) · P(B).
B. P(A and B) = P(A) + P(B).
C. P(A/B) = P(B).
D. P(B/A) = P(A).
E. P(A or B) = P(A) · P(B).

If A and B are independent events with P(A) = 0.25 and P(B) = 0.60, then P(A/B) is:
A. 0.25.
B. 0.60.
C. 0.35.
D. 0.85.
E. 0.15

If the probability of drawing an Ace from a deck of cards is 0.077 and the probability of rolling a “2” using a fair die is 0.167, then the probability of drawing an Ace and rolling a “2” is
A. 0.244
B. 0.090
C. 0.454
D. 0.013
E. 0.333

The joint probability of Events A and B is described as:
A. The probability of Event A, given that Event B has occurred.
B. The probability of Event B, given that Event A has occurred.
C. The probability that either Event A or Event B has occurred.
D. The probability that both Event A and Event B has occurred.

A survey revealed that 21.5% of the households had no checking account, 66.9% had regular checking accounts, and 11.6% had NOW accounts. Of those households with no checking account 40% had savings accounts. Of the households with regular checking accounts 71.6% had a savings account. Of the households with NOW accounts 79.3% had savings accounts.
The probability that a randomly selected household has a savings account is:
A. 0.609.
B. 1.000.
C. 0.227.
D. 0.657.
E. 0.537.

A survey revealed that 21.5% of the households had no checking account, 66.9% had regular checking accounts, and 11.6% had NOW accounts. Of those households with no checking account 40% had savings accounts. Of the households with regular checking accounts 71.6% had a savings account. Of the households with NOW accounts 79.3% had savings accounts.
The probability that a randomly selected household has no checking account and no savings account is:
A. 0.0860.
B. 0.1290.
C. 0.5330.
D. 0.1309.
E. 0.3430.

A survey revealed that 21.5% of the households had no checking account, 66.9% had regular checking accounts, and 11.6% had NOW accounts. Of those households with no checking account 40% had savings accounts. Of the households with regular checking accounts 71.6% had a savings account. Of the households with NOW accounts 79.3% had savings accounts.
The probability that a randomly selected household with a savings account has no checking account is:
A. 0.1309.
B. 0.1290.
C. 0.1437.
D. 0.2150.
E. 0.4000.

Which of the following statements is correct given that the events A and B have nonzero probabilities?
A. A and B cannot be both independent and mutually exclusive
B. A and B can be both independent and mutually exclusive
C. A and B are always independent
D. A and B are always mutually exclusive

The odds of the Dallas Cowboys winning this year’s Super Bowl are 3 to 1. Compute the probability of the Cowboys winning.
________________________________________

The table below indicates the number of majors found in a college of business:
What is the probability that a randomly selected student is an accounting major?
________________________________________

The table below indicates the number of majors found in a college of business:
What is the probability that a randomly selected student is either a computer science major or a marketing major?
________________________________________

The table below indicates the number of majors found in a college of business:
What is the probability that a randomly selected student is a finance major and an accounting major?
________________________________________

An appliance dealer calculated the proportion of new dishwashers sold that required various numbers of service calls to correct problems during the warranty period. The records were:
Let X be the number of service calls during the warranty period for a dishwasher. What is the probability that there will be at least one service call but not more than 3?
________________________________________

An appliance dealer calculated the proportion of new dishwashers sold that required various numbers of service calls to correct problems during the warranty period. The records were:
Let X be the number of service calls during the warranty period for a dishwasher. What is the probability that there will be between two and four (inclusive) service calls?
________________________________________

An appliance dealer calculated the proportion of new dishwashers sold that required various numbers of service calls to correct problems during the warranty period. The records were:
Let X be the number of service calls during the warranty period for a dishwasher. What is the probability that there will be exactly one service call?
________________________________________

An appliance dealer calculated the proportion of new dishwashers sold that required various numbers of service calls to correct problems during the warranty period. The records were:
Let X be the number of service calls during the warranty period for a dishwasher. What is the probability that there will be at least one service call?
________________________________________

An appliance dealer calculated the proportion of new dishwashers sold that required various numbers of service calls to correct problems during the warranty period. The records were:
Let X be the number of service calls during the warranty period for a dishwasher. What is the probability that there will be at most one service call?
________________________________________

A personnel manager is reviewing number of overtime hours worked by employees in her plant. She has compiled the following data:
For a randomly selected employee let X be the number of overtime hours worked, and define the following events:

A = employee who works no overtime.

B = employee who works at least 7 hours overtime.

C = employee who works at most 4 hours overtime.

Determine the probability of event A.
________________________________________

A personnel manager is reviewing number of overtime hours worked by employees in her plant. She has compiled the following data:
For a randomly selected employee let X be the number of overtime hours worked, and define the following events:

A = employee who works no overtime.

B = employee who works at least 7 hours overtime.

C = employee who works at most 4 hours overtime.

Determine the probability of event B.
________________________________________

A personnel manager is reviewing number of overtime hours worked by employees in her plant. She has compiled the following data:
For a randomly selected employee let X be the number of overtime hours worked, and define the following events:

A = employee who works no overtime.

B = employee who works at least 7 hours overtime.

C = employee who works at most 4 hours overtime.

Determine the probability of event C.
________________________________________

The odds in favor of an event are the number of successes divided by the number of failures. The probability of this event occurring is the number of successes divided by the sum of the number of successes and the number of failures. The number of successes is five and the number of failures is four.
Find the probability of failure.
________________________________________

A shoe store carries 590 pairs of Stacy-Adams and 610 pairs of Freeman brands of shoes. Let a success be the event of randomly selecting a pair of Stacy-Adams shoes.
Find the probability of a success.
________________________________________

In the board game called TRIVIAL PURSUIT, a single die is used to determine the number of spaces a player is allowed to move. A player is currently positioned 3 spaces from a space where a correct answer will earn a “pie” and 4 spaces from a space where “roll again” is the option. Assuming a fair die, what is the probability the player will get to answer a question for a “pie” or get to “roll again”?
________________________________________

Find P (C1 and D1).
________________________________________

Find P (D1) or P (C1).
________________________________________

Find P (C1 or D1).
________________________________________

Find P (D1 or D2 or D3).
________________________________________

Six candidates for a new position of vice-president for academic affairs have been selected. Three of the candidates are female. The candidates’ years of experience are as follows:
Suppose one of the candidates is selected at random. Define the following events:

A = person selected has 9 years experience.

B = person selected is a female.

Find P(A).
________________________________________

Six candidates for a new position of vice-president for academic affairs have been selected. Three of the candidates are female. The candidates’ years of experience are as follows:
Suppose one of the candidates is selected at random. Define the following events:

A = person selected has 9 years experience.

B = person selected is a female.

Find P(B).
________________________________________

Six candidates for a new position of vice-president for academic affairs have been selected. Three of the candidates are female. The candidates’ years of experience are as follows:
Suppose one of the candidates is selected at random. Define the following events:

A = person selected has 9 years experience.

B = person selected is a female.

Find P(A / B).
________________________________________

Six candidates for a new position of vice-president for academic affairs have been selected. Three of the candidates are female. The candidates’ years of experience are as follows:
Suppose one of the candidates is selected at random. Define the following events:

A = person selected has 9 years experience.

B = person selected is a female.

Find P(not A / B).
________________________________________

A large men’s store in a mall purchases suits from four different manufacturers in short, regular, and long. Their current selections are given in the contingency table below:
Let the abbreviations and letters represent the events. For example Event S = a randomly selected suit is short, event HMS = a randomly selected suit is manufactured by HMS.

Compute P(S).
________________________________________

A large men’s store in a mall purchases suits from four different manufacturers in short, regular, and long. Their current selections are given in the contingency table below:
Let the abbreviations and letters represent the events. For example Event S = a randomly selected suit is short, event HMS = a randomly selected suit is manufactured by HMS.

Compute P(HMS).
________________________________________

A large men’s store in a mall purchases suits from four different manufacturers in short, regular, and long. Their current selections are given in the contingency table below:
Let the abbreviations and letters represent the events. For example Event S = a randomly selected suit is short, event HMS = a randomly selected suit is manufactured by HMS.

Compute P(S and HMS).
________________________________________

A large men’s store in a mall purchases suits from four different manufacturers in short, regular, and long. Their current selections are given in the contingency table below:
Let the abbreviations and letters represent the events. For example Event S = a randomly selected suit is short, event HMS = a randomly selected suit is manufactured by HMS.

Compute P(S /HMS).
________________________________________

A large men’s store in a mall purchases suits from four different manufacturers in short, regular, and long. Their current selections are given in the contingency table below:
Let the abbreviations and letters represent the events. For example Event S = a randomly selected suit is short, event HMS = a randomly selected suit is manufactured by HMS.

Compute P(HMS / S).
________________________________________

A political telephone survey of 360 people asked whether they were in favor or not in favor of a proposed law. Each person was identified as either Republican or Democrat. The results are shown in the following table:

Party	In Favor	Not in Favor	Undecided	Total
Republican	98	54	40	192
Democrat	79	29	60	168
Total	177	83	100	360

What is the probability that a randomly selected respondent was in favor of the proposed law?
________________________________________

A political telephone survey of 360 people asked whether they were in favor or not in favor of a proposed law. Each person was identified as either Republican or Democrat. The results are shown in the following table:

Party	In Favor	Not in Favor	Undecided	Total
Republican	98	54	40	192
Democrat	79	29	60	168
Total	177	83	100	360

What is the probability that a randomly selected respondent was a Democrat?
________________________________________

A political telephone survey of 360 people asked whether they were in favor or not in favor of a proposed law. Each person was identified as either Republican or Democrat. The results are shown in the following table:

Party	In Favor	Not in Favor	Undecided	Total
Republican	98	54	40	192
Democrat	79	29	60	168
Total	177	83	100	360

What is the probability that a randomly selected respondent was a Republican and undecided about the proposed law?
________________________________________

A political telephone survey of 360 people asked whether they were in favor or not in favor of a proposed law. Each person was identified as either Republican or Democrat. The results are shown in the following table:

Party	In Favor	Not in Favor	Undecided	Total
Republican	98	54	40	192
Democrat	79	29	60	168
Total	177	83	100	360

What is the probability that a randomly selected respondent was a Democrat or not in favor of the proposed law?
________________________________________

A political telephone survey of 360 people asked whether they were in favor or not in favor of a proposed law. Each person was identified as either Republican or Democrat. The results are shown in the following table:

Party	In Favor	Not in Favor	Undecided	Total
Republican	98	54	40	192
Democrat	79	29	60	168
Total	177	83	100	360

Given that the respondent was in favor of the proposed law, what is the probability that they were a Republican?
________________________________________

A Gulf Coast travel park has the following accommodations:

Number of Bedrooms
Location	3 Bedroom	4 Bedroom	Total
Beach Front	17	24	41
Non Beach Front	6	210	216
Total	23	234	257

What is the probability of selecting a beachfront site?
________________________________________

A Gulf Coast travel park has the following accommodations:

Number of Bedrooms
Location	3 Bedroom	4 Bedroom	Total
Beach Front	17	24	41
Non Beach Front	6	210	216
Total	23	234	257

What is the probability of selecting a non beach front site with 3 bedrooms?
________________________________________

A Gulf Coast travel park has the following accommodations:

Number of Bedrooms
Location	3 Bedroom	4 Bedroom	Total
Beach Front	17	24	41
Non Beach Front	6	210	216
Total	23	234	257

What is the probability of selecting a non beach front site given that the facility had 4 bedrooms?
________________________________________

The physical science degrees conferred by a school between 1992 and 1995 were broken down as follows:
Suppose a person is selected at random from these graduates. Consider the following events:

M: The person is a male.

F: The person is a female.

P: The person graduated in physics.

C: The person graduated in chemistry.

G: The person graduated in geology.

Find P(M).
________________________________________

The physical science degrees conferred by a school between 1992 and 1995 were broken down as follows:
Suppose a person is selected at random from these graduates. Consider the following events:

M: The person is a male.

F: The person is a female.

P: The person graduated in physics.

C: The person graduated in chemistry.

G: The person graduated in geology.

Find P(M / P).
________________________________________

The physical science degrees conferred by a school between 1992 and 1995 were broken down as follows:
Suppose a person is selected at random from these graduates. Consider the following events:

M: The person is a male.

F: The person is a female.

P: The person graduated in physics.

C: The person graduated in chemistry.

G: The person graduated in geology.

Find P(M and P).
________________________________________

The physical science degrees conferred by a school between 1992 and 1995 were broken down as follows:
Suppose a person is selected at random from these graduates. Consider the following events:

M: The person is a male.

F: The person is a female.

P: The person graduated in physics.

C: The person graduated in chemistry.

G: The person graduated in geology.

Find P(C / F).
________________________________________

A study of Brand D washing machines that failed within three years (warranty period) was 23.2%. Of those that failed, 82.9% lasted over two years. What is the probability that a washer, which lasts at least two years, will still fail before the end of the warranty period?
________________________________________

A firm produces three qualities of bed linens — good, better, best. Production is scheduled to result in 50% good, 35% better, and 15% best. A quality control person checks the finished product and classified them as acceptable or imperfect. The percentages acceptable are good, 92%; better, 88%; best, 82%. Find the posterior probability that a sheet, which is “acceptable”, will be acceptable.
________________________________________

The prior probabilities for two events A₁ and A₂ are P(A₁) = .30 and P(A₂) = .70. It is also known that P(A₁ and A₂) = 0. Suppose P(B / A₁) = .15 and P(B / A₂) = .05.
Compute P(A₁ and B).
________________________________________

The prior probabilities for two events A₁ and A₂ are P(A₁) = .30 and P(A₂) = .70. It is also known that P(A₁ and A₂) = 0. Suppose P(B / A₁) = .15 and P(B / A₂) = .05.
Compute P(A₂ and B).
________________________________________

The prior probabilities for two events A₁ and A₂ are P(A₁) = .30 and P(A₂) = .70. It is also known that P(A₁ and A₂) = 0. Suppose P(B / A₁) = .15 and P(B / A₂) = .05.
Compute P(B).
________________________________________

The prior probabilities for two events A₁ and A₂ are P(A₁) = .30 and P(A₂) = .70. It is also known that P(A₁ and A₂) = 0. Suppose P(B / A₁) = .15 and P(B / A₂) = .05.
Apply Bayes’ theorem to compute P(A₁ / B).
________________________________________

The prior probabilities for two events A₁ and A₂ are P(A₁) = .30 and P(A₂) = .70. It is also known that P(A₁ and A₂) = 0. Suppose P(B / A₁) = .15 and P(B / A₂) = .05.
Apply Bayes’ theorem to compute P(A₂ / B).
________________________________________

The prior probabilities of events A₁, A₂, and A₃ are P(A₁) = .50, P(A₂) = .20 and P(A₃) = .30. The conditional probabilities of event B given A₁, A₂, and A₃ are P(B / A₁) = .40, P(B / A₂) = .50 and P(B / A₃) = .30.
Compute P(B and A₁).
________________________________________

The prior probabilities of events A₁, A₂, and A₃ are P(A₁) = .50, P(A₂) = .20 and P(A₃) = .30. The conditional probabilities of event B given A₁, A₂, and A₃ are P(B / A₁) = .40, P(B / A₂) = .50 and P(B / A₃) = .30.
Compute P(B and A₂).
________________________________________

The prior probabilities of events A₁, A₂, and A₃ are P(A₁) = .50, P(A₂) = .20 and P(A₃) = .30. The conditional probabilities of event B given A₁, A₂, and A₃ are P(B / A₁) = .40, P(B / A₂) = .50 and P(B / A₃) = .30.
Compute P(B and A₃).
________________________________________

The prior probabilities of events A₁, A₂, and A₃ are P(A₁) = .50, P(A₂) = .20 and P(A₃) = .30. The conditional probabilities of event B given A₁, A₂, and A₃ are P(B / A₁) = .40, P(B / A₂) = .50 and P(B / A₃) = .30.
Compute P(B).
________________________________________

The prior probabilities of events A₁, A₂, and A₃ are P(A₁) = .50, P(A₂) = .20 and P(A₃) = .30. The conditional probabilities of event B given A₁, A₂, and A₃ are P(B / A₁) = .40, P(B / A₂) = .50 and P(B / A₃) = .30.
Apply Bayes’ theorem to compute the posterior probability P(A₁ / B).
________________________________________

The prior probabilities of events A₁, A₂, and A₃ are P(A₁) = .50, P(A₂) = .20 and P(A₃) = .30. The conditional probabilities of event B given A₁, A₂, and A₃ are P(B / A₁) = .40, P(B / A₂) = .50 and P(B / A₃) = .30.
Apply Bayes’ theorem to compute the posterior probability P(A₂ / B).
________________________________________

The prior probabilities of events A₁, A₂, and A₃ are P(A₁) = .50, P(A₂) = .20 and P(A₃) = .30. The conditional probabilities of event B given A₁, A₂, and A₃ are P(B / A₁) = .40, P(B / A₂) = .50 and P(B / A₃) = .30.
Apply Bayes’ theorem to compute the posterior probability P(A₃ / B).
________________________________________

An investment counselor would like to meet with 14 of his clients on Wednesday, but he only has time for 10 appointments. How many different combinations of the clients could be considered for inclusion into his limited schedule for that day?
________________________________________

How many different combinations are possible if 8 substitute workers are available to fill 4 openings created by employees planning to take vacation leave next week?
________________________________________

Ten students from an economics class have formed a study group. Each may or may not attend a study session. Assuming that the members will be making independent decisions on whether or not to attend, how many different possibilities exist for the composition of the study session?
________________________________________

A state’s license plate has 9 positions, each of which has 37 possibilities (26 letters, 10 integers, or blank). If the purchaser of a vanity plate wants his first seven positions to be Stanley, in how many ways can his plate appear?
________________________________________

The following represent interest rates on 20 U.S. Treasury bond issues with maturity dates in 2000-2001, as listed in Money Magazine:
Determine the probability that a randomly selected bond will have a rate of interest between 11 and 12 percent.
________________________________________

The following represent interest rates on 20 U.S. Treasury bond issues with maturity dates in 2000-2001, as listed in Money Magazine:
Determine the probability that a randomly selected bond will have a rate of interest of ten percent up to but not including 14 percent.
________________________________________

The following represent interest rates on 20 U.S. Treasury bond issues with maturity dates in 2000-2001, as listed in Money Magazine:
Determine the probability that a randomly selected bond will have a rate of interest of at least 14 percent, but less than 15 percent.
________________________________________

The following represent interest rates on 20 U.S. Treasury bond issues with maturity dates in 2000-2001, as listed in Money Magazine:
Determine the probability that a randomly selected bond will have a rate of interest of less than 13 percent.
________________________________________

The following represent interest rates on 20 U.S. Treasury bond issues with maturity dates in 2000-2001, as listed in Money Magazine:
Determine the probability that a randomly selected bond will have a rate of interest of 11 percent or more.
________________________________________

The following represent interest rates on 20 U.S. Treasury bond issues with maturity dates in 2000-2001, as listed in Money Magazine:
Using the letter identifications, calculate P (A or F).
________________________________________

The following represent interest rates on 20 U.S. Treasury bond issues with maturity dates in 2000-2001, as listed in Money Magazine:
Using the letter identifications, calculate P (B and D).
________________________________________

The Burger Queen Company has 124 locations along the west coast. The general manager is concerned with the profitability of the locations compared with major menu items sold. The information below shows the number of each menu item selected by profitability of store.
If a menu item is selected at random, what is the probability that the store is a high profit store?
________________________________________

The Burger Queen Company has 124 locations along the west coast. The general manager is concerned with the profitability of the locations compared with major menu items sold. The information below shows the number of each menu item selected by profitability of store.
What is the probability that an item selected at random is a Mother burger?
________________________________________

The Burger Queen Company has 124 locations along the west coast. The general manager is concerned with the profitability of the locations compared with major menu items sold. The information below shows the number of each menu item selected by profitability of store.
What is the probability of selecting a menu item from a high profit store and it is nachos?
________________________________________

The Burger Queen Company has 124 locations along the west coast. The general manager is concerned with the profitability of the locations compared with major menu items sold. The information below shows the number of each menu item selected by profitability of store.
What is the probability of tacos being selected at a low profit store?
________________________________________

Intentions of consumers regarding future automobile purchases and the financial capability of the consumers are given below:
For a randomly selected consumer, find the following probability: P(D).
________________________________________

Intentions of consumers regarding future automobile purchases and the financial capability of the consumers are given below:
For a randomly selected consumer, find the following probability: P(B and D).
________________________________________

Intentions of consumers regarding future automobile purchases and the financial capability of the consumers are given below:
For a randomly selected consumer, find the following probability: P(A and D).
________________________________________

Intentions of consumers regarding future automobile purchases and the financial capability of the consumers are given below:
For a randomly selected consumer, find the following probability: P(A or D).
________________________________________

Intentions of consumers regarding future automobile purchases and the financial capability of the consumers are given below:
For a randomly selected consumer, find the following probability: P(A / D).
________________________________________

Intentions of consumers regarding future automobile purchases and the financial capability of the consumers are given below:
For a randomly selected consumer, find the following probability: P(E / B).
________________________________________

A dormitory has two activating devices in each fire detector. One is smoke activated and has a probability of .98 of sounding an alarm when it should. The second is a heat sensitive activator and has a probability of .95 of operating when it should. Each activator operates independently of the other. Presume a fire starts near a detector.
What is the probability that the detector will sound an alarm?
________________________________________

A dormitory has two activating devices in each fire detector. One is smoke activated and has a probability of .98 of sounding an alarm when it should. The second is a heat sensitive activator and has a probability of .95 of operating when it should. Each activator operates independently of the other. Presume a fire starts near a detector.
What is the probability that both types of activators will work properly?
________________________________________

A dormitory has two activating devices in each fire detector. One is smoke activated and has a probability of .98 of sounding an alarm when it should. The second is a heat sensitive activator and has a probability of .95 of operating when it should. Each activator operates independently of the other. Presume a fire starts near a detector.
What is the probability that only the smoke activator functions?
________________________________________

____________________ probabilities find their greatest application in games of chance, but they are not so useful when the underlying processes are not well known.
________________________________________

Because we can determine the probability without actually engaging in any experiments, the classical approach is also referred to as the ____________________ approach.
________________________________________

The relative frequency approach to probability depends on the law of ______________________________.
________________________________________

Probability refers to a number between ____________________ and ____________________ which expresses the ____________________ that an event will occur.
________________________________________

You have applied for a job and are told by the interviewer that the probability of your being hired is 0.70. Calculate the odds that you will be hired.
The odds are ____________________ to ____________________.
________________________________________

The probability of a tornado hitting in your city has been estimated at 0.001. What are the corresponding odds?
The odds are ____________________ to ____________________.
________________________________________

In a state lottery, which pays at least one million dollars, six numbers from 1 to 50 are randomly selected. If five have been selected and your ticket matches the first five, what are the odds that the sixth number will make you a millionaire?
The odds are ____________________ to ____________________.
________________________________________

The grade distribution for a particular statistics exam was recorded as follows:

Grade	Number of Students
90-100	10
80-89	10
70-79	8
60-69	2
Total	30

The probability that a randomly selected student received an “A” was found to be 33%. This is an example of __________________________________________________ approach to probability.
________________________________________

An event A and its complement A‘ are always ___________________________________.
________________________________________

A set of events is ____________________ if it includes all the possible outcomes of an experiment.
________________________________________

The ____________________ of events describes the case where two or more events occur at the same time.
________________________________________

When we wish to determine the probability that one or more of several events will occur in an experiment, we would use ____________________ rules.
________________________________________

When events are ____________________ the occurrence of one means that none of the others can occur.
________________________________________

Events are ____________________ when the occurrence of one event has no effect on the probability that another will occur.
________________________________________

Events are ____________________ when the occurrence of one event changes the probability that another will occur.
________________________________________

The physical science degrees conferred by a school between 1992 and 1995 were broken down as follows:
Suppose a person is selected at random from these graduates. Consider the following events:

M: The person is a male.

F: The person is a female.

P: The person graduated in physics.

C: The person graduated in chemistry.

G: The person graduated in geology.

Complete the formula: P(M / P) = P(P and M) / ____________________.
________________________________________

____________________ refer to the number of different ways in which objects can be arranged in order.
________________________________________

____________________ consider only the possible sets of objects, regardless of the order in which the members of the set are arranged.
________________________________________

The odds in favor of an event are the number of successes divided by the number of failures. The probability of this event occurring is the number of successes divided by the sum of the number of successes and the number of failures. The number of successes is five and the number of failures is four.
Find the odds in favor of success.

The odds are ____________________ to ____________________.
________________________________________

A shoe store carries 590 pairs of Stacy-Adams and 610 pairs of Freeman brands of shoes. Let a success be the event of randomly selecting a pair of Stacy-Adams shoes.
Find the odds of selecting a pair of Stacy-Adams shoes.

The odds are ____________________ to ____________________.
________________________________________

If the odds in favor of an event happening are A:B, what is the probability being expressed?

You think you have a 95% chance of passing your next business statistics exam. This is an example of which approach to probability?

Create a Venn diagram illustrating an Event A, and its complement.

From an ordinary deck of 52 playing cards one is selected at random. Define the following events:
A = card selected is an Ace.

B = card selected is a Queen.

C = card selected is a three.

Are A, B, and C mutually exclusive events?

Use the addition rule to find P(A or B or C).

According to an old song lyric, “love and marriage go together like a horse and carriage.” Let love be event A and marriage be event B. Are events A and B mutually exclusive?

One card is randomly selected from a deck of 52 playing cards. Define the following events:
A = card selected is a five.

B = card selected is a ten.

C = card selected is a jack.

Find P(not A or not B or not C) using the addition rule.

Six candidates for a new position of vice-president for academic affairs have been selected. Three of the candidates are female. The candidates’ years of experience are as follows:
Suppose one of the candidates is selected at random. Define the following events:

A = person selected has 9 years experience.

B = person selected is a female.

Are events A and B independent? Explain using probability.

A Gulf Coast travel park has the following accommodations:

Number of Bedrooms
Location	3 Bedroom	4 Bedroom	Total
Beach Front	17	24	41
Non Beach Front	6	210	216
Total	23	234	257

Is the event of selecting a beach front site independent of the event of selecting a 3 bedroom facility? Explain.

The physical science degrees conferred by a school between 1992 and 1995 were broken down as follows:
Suppose a person is selected at random from these graduates. Consider the following events:

M: The person is a male.

F: The person is a female.

P: The person graduated in physics.

C: The person graduated in chemistry.

G: The person graduated in geology.

Are the events C and F independent?

The physical science degrees conferred by a school between 1992 and 1995 were broken down as follows:
Suppose a person is selected at random from these graduates. Consider the following events:

M: The person is a male.

F: The person is a female.

P: The person graduated in physics.

C: The person graduated in chemistry.

G: The person graduated in geology.

Explain why events C and F are or are not independent.

The prior probabilities for two events A₁ and A₂ are P(A₁) = .30 and P(A₂) = .70. It is also known that P(A₁ and A₂) = 0. Suppose P(B / A₁) = .15 and P(B / A₂) = .05.
Are A₁ and A₂ mutually exclusive? Explain.

Machine A produces 3% defectives, machine B produces 5% defectives, and machine C produces 10% defectives. Of the total output from these machines, 60% of the items are from machine A, 30% from B, and 10% from C. One item is selected at random from a day’s production.
What is the prior probability that the item came from machine A?

Machine B?

Machine C?

Machine A produces 3% defectives, machine B produces 5% defectives, and machine C produces 10% defectives. Of the total output from these machines, 60% of the items are from machine A, 30% from B, and 10% from C. One item is selected at random from a day’s production.
What is the probability that the item is defective?

Machine A produces 3% defectives, machine B produces 5% defectives, and machine C produces 10% defectives. Of the total output from these machines, 60% of the items are from machine A, 30% from B, and 10% from C. One item is selected at random from a day’s production.
If inspection finds the item to be defective, what is the revised probability that the item came from machine C?

Machine A produces 3% defectives, machine B produces 5% defectives, and machine C produces 10% defectives. Of the total output from these machines, 60% of the items are from machine A, 30% from B, and 10% from C. One item is selected at random from a day’s production.
If inspection finds the item to be defective, what is the revised probability that the item came from machine B?

Machine A produces 3% defectives, machine B produces 5% defectives, and machine C produces 10% defectives. Of the total output from these machines, 60% of the items are from machine A, 30% from B, and 10% from C. One item is selected at random from a day’s production.
If inspection finds the item to be defective, what is the revised probability that the item came from machine A?

I would like to select 3 paperback books from a list of 12 books to take on vacation. How many different sets of 3 books can I choose?

At a track meet, eight runners are competing in the 100-yard dash. First, second, and third trophies will be awarded. In how many ways can the trophies be awarded?

In advertising a mountain cabin near Keystone, Colorado, a property owner can specify (1) whether or not pets are permitted, (2) whether the rent is based on off-season, during summer season, or during the Dec.-Jan. peak skiing season, (3) whether or not children under 12 are allowed, and (4) whether the minimum stay is for 4, 7, or 10 days. How many different versions of the ad can be generated?

The Burger Queen Company has 124 locations along the west coast. The general manager is concerned with the profitability of the locations compared with major menu items sold. The information below shows the number of each menu item selected by profitability of store.
If a menu order is selected at random, describe the following in words.

A) P(M5)

B) P(R3)

C) P(R2 and M3)

D) P(M2 / R2)

E) P(R1 / M4)

The Burger Queen Company has 124 locations along the west coast. The general manager is concerned with the profitability of the locations compared with major menu items sold. The information below shows the number of each menu item selected by profitability of store.
Is the sale of Mother Burgers independent of profitability of store?

The Burger Queen Company has 124 locations along the west coast. The general manager is concerned with the profitability of the locations compared with major menu items sold. The information below shows the number of each menu item selected by profitability of store.
What item was the favorite in a medium profit store?

What percentage of the time was this item selected?

The Burger Queen Company has 124 locations along the west coast. The general manager is concerned with the profitability of the locations compared with major menu items sold. The information below shows the number of each menu item selected by profitability of store.
What item was selected the least at any type store?

What percentage of the time was this item selected?

The Burger Queen Company has 124 locations along the west coast. The general manager is concerned with the profitability of the locations compared with major menu items sold. The information below shows the number of each menu item selected by profitability of store.
What item has the highest probability of being selected for any type store?

What percentage of the time was this item selected?

The Burger Queen Company has 124 locations along the west coast. The general manager is concerned with the profitability of the locations compared with major menu items sold. The information below shows the number of each menu item selected by profitability of store.
Determine the probability for:

A) P(M5)

B) P(R3)

C) P(R2 and M3)

D) P(M2 / R2)

E) P(R1 / M4)

An investment firm has classified its clients according to their gender and the composition of their investment portfolio (primarily bonds, primarily stocks, or a balanced mix of bonds and stocks). The proportions of clients falling into the various categories are shown in the following table:

Portfolio Composition
Gender	Bonds	Stocks	Balanced
Male	0.18	0.20	0.25
Female	0.12	0.05	0.20

One client is selected at random, and two events A and B are defined as follows:

A: The client selected is male.

B: The client selected has a balanced portfolio.

Express each of the following events in words:

A) A or B

B) A and B

C) A and

D) or

An investment firm has classified its clients according to their gender and the composition of their investment portfolio (primarily bonds, primarily stocks, or a balanced mix of bonds and stocks). The proportions of clients falling into the various categories are shown in the following table:

Portfolio Composition
Gender	Bonds	Stocks	Balanced
Male	0.18	0.20	0.25
Female	0.12	0.05	0.20

One client is selected at random, and two events A and B are defined as follows:

A: The client selected is male.

B: The client selected has a balanced portfolio.

Find the following probabilities:

A) P(A)

B) P(B)

An investment firm has classified its clients according to their gender and the composition of their investment portfolio (primarily bonds, primarily stocks, or a balanced mix of bonds and stocks). The proportions of clients falling into the various categories are shown in the following table:

Portfolio Composition
Gender	Bonds	Stocks	Balanced
Male	0.18	0.20	0.25
Female	0.12	0.05	0.20

One client is selected at random, and two events A and B are defined as follows:

A: The client selected is male.

B: The client selected has a balanced portfolio.

Find the following probabilities:

A) P(A or B)

B) P(A and B)

An investment firm has classified its clients according to their gender and the composition of their investment portfolio (primarily bonds, primarily stocks, or a balanced mix of bonds and stocks). The proportions of clients falling into the various categories are shown in the following table:

Portfolio Composition
Gender	Bonds	Stocks	Balanced
Male	0.18	0.20	0.25
Female	0.12	0.05	0.20

One client is selected at random, and two events A and B are defined as follows:

A: The client selected is male.

B: The client selected has a balanced portfolio.

Express each of the following probabilities in words:

A) P(A/B)

B) P(B/A)

An investment firm has classified its clients according to their gender and the composition of their investment portfolio (primarily bonds, primarily stocks, or a balanced mix of bonds and stocks). The proportions of clients falling into the various categories are shown in the following table:

Portfolio Composition
Gender	Bonds	Stocks	Balanced
Male	0.18	0.20	0.25
Female	0.12	0.05	0.20

One client is selected at random, and two events A and B are defined as follows:

A: The client selected is male.

B: The client selected has a balanced portfolio.

Find the following probabilities:

A) P(A/B)

B) P(B/A)

An investment firm has classified its clients according to their gender and the composition of their investment portfolio (primarily bonds, primarily stocks, or a balanced mix of bonds and stocks). The proportions of clients falling into the various categories are shown in the following table:

Portfolio Composition
Gender	Bonds	Stocks	Balanced
Male	0.18	0.20	0.25
Female	0.12	0.05	0.20

One client is selected at random, and two events A and B are defined as follows:

A: The client selected is male.

B: The client selected has a balanced portfolio.

Are A and B independent events? Explain.

An investment firm has classified its clients according to their gender and the composition of their investment portfolio (primarily bonds, primarily stocks, or a balanced mix of bonds and stocks). The proportions of clients falling into the various categories are shown in the following table:

Portfolio Composition
Gender	Bonds	Stocks	Balanced
Male	0.18	0.20	0.25
Female	0.12	0.05	0.20

One client is selected at random, and two events A and B are defined as follows:

A: The client selected is male.

B: The client selected has a balanced portfolio.

Are A and B mutually exclusive events? Explain.

There are 12 players on a basketball team and 5 of those players start the game. How many different starting lineups are possible?

What is the subjective approach to probability?

Explain the relationship between a relative-frequency distribution and a probability distribution for any numerical population.

Identify the following type of graphic, and describe what it illustrates:

Define contingency table.

Define marginal probability.

Define conditional probability.

Write a word statement for P (B / A).

State in your own words the probability concept of independence.

Express the probability concept of independence for events A and B in marginal and conditional probabilities.

Chapter 5: Probability: Review of Basic Concepts Key

True or False
Uncertainty plays an important role in our daily lives and activities as well as in business.
TRUE

True or False
In the classical approach, probability is the proportion of times an event is observed to occur in a very larger number of trials.
FALSE

True or False
Sometimes it is useful to revise a probability on the basis of additional information that we didn’t have before.
TRUE

True or False
An experiment is an activity of measurement that results in an outcome.
TRUE

True or False
In general, an event is one of the possible outcomes of an experiment.
FALSE

True or False
The relative frequency approach to probability is judgmental, representing the degree to which one happens to believe that an event will or will not happen.
FALSE

If the probability of an event is x, with , then the odds in favor of the event are x to (1 – x).
TRUE

True or False
The union of events describes two or more events occurring at the same time.
FALSE

True or False
When the events within a set are both mutually exclusive and exhaustive, the sum of their probabilities is 1.0.
TRUE

True or False
When events are mutually exclusive, two or more of them can happen at the same time.
FALSE

True or False
If P(A) = 0.5 and P(B) = 0.80, then P(A or B) must be 0.95.
FALSE

True or False
When events A and B are independent, then P(A and B) = P(A) + P(B).
FALSE

True or False
Bayes’ theorem is an extension of the concept of conditional probability.
TRUE

True or False
Prior probability is a marginal probability while posterior probability is a conditional probability.
TRUE

If the event of interest is A, then:
A.the probability that A will not occur is [1 – P(A)].
B. the probability that A will not occur is the complement of A.
C. the probability is zero if event A is impossible.
D. the probability is one if event A is certain.
E. All of these are true.

The classical approach describes a probability:
A.in terms of the proportion of times an event is observed to occur in a very large number of trials.
B. in terms of the degree to which one happens to believe that an event will happen.
C. in terms of the proportion of times that an event can be theoretically expected to occur.
D. is dependent on the law of large numbers.
E. describes an event for which all outcomes are equally likely.

An example of the classical approach to probability would be:
A.the estimate of number of defective parts based on previous production data.
B. your estimate of the probability of a pop quiz in class on a given day.
C. the annual estimate of the number of deaths of persons age 25.
D. the probability of drawing an Ace from a deck of cards.

If a set of events includes all the possible outcomes of an experiment, these events are considered to be:
A.mutually exclusive.
B. exhaustive.
C. intersecting.
D. inclusive.
E. None of the above.

A student is randomly selected from a class. Event A = the student is a male and Event B = the student is a female. Events A and B are:
A.mutually exclusive.
B. exhaustive.
C. intersecting.
D. dependent.
E. both A and B.

Which of the following is not an approach to assigning probabilities?
A.The Classical approach
B. The Trial and error approach
C. The Relative frequency approach
D. The Subjective approach
E. All of the above are approaches to assigning probabilities.

If Events A and B are not mutually exclusive, then the probability that one of the events will occur is represented by
A.P(A or B) = P(A) + P(B) – P(A and B)
B. P(A or B) = P(A) + P(B)
C. P(A and B) = P(A) + P(B) – P(A or B)
D. P(A and B) = P(A) + P(B)
E. P(A or B) = P(A) + P(B) + P(A and B)

Which of the following statements is not correct?
A.Two events A and B are mutually exclusive if event A occurs and event B cannot occur.
B. If events A and B occur at the same time, then A and B intersect.
C. If event A does not occur, then its complement A‘ will also not occur.
D. A union of events occurs when at least one event in a group occurs, e.g., (A or B or C).
E. If all possible outcomes of an experiment are represented in a set, the set is considered exhaustive.

If a contingency table shows the sex and classification of undergraduate students (freshman, sophomore, junior, senior) in your statistics class, which of the following is true?
A.The sex of the student is an example of mutually exclusive events.
B. Because yours is an undergraduate class, the events are exhaustive, i.e., each student must fall in one of the classifications.
C. An example for the intersection of events would be the number of males who are juniors.
D. An example for the union of events would be the number of students who are female or juniors.
E. All of these are true.

The table below gives the probabilities of combinations of religion and political parties in a major U.S. city.
Which of the following represents two mutually exclusive events?
A.(A and D).
B. (A and E).
C. (A and F).
D. (A and G).
E. All of these are mutually exclusive.

The table below gives the probabilities of combinations of religion and political parties in a major U.S. city.
Which two of the following pairs of events intersect?
A.A and D
B. A and E
C. F and E
D. B and C
E. D and B

The table below gives the probabilities of combinations of religion and political parties in a major U.S. city.
What is the probability that a randomly selected person would be a Protestant and at the same time be a Democrat or a Republican?
A.0.67
B. 0.35
C. 0.95
D. 0.89
E. 0.62

The table below gives the probabilities of combinations of religion and political parties in a major U.S. city.
What is the probability that a randomly selected person would be an independent whose religion was neither Protestant nor Catholic?
A.0.05
B. 0.03
C. 0.02
D. 0.01

The table below gives the probabilities of combinations of religion and political parties in a major U.S. city.
What is the probability that a randomly selected person would be a Democrat who was not Jewish?
A.0.93
B. 0.50
C. 0.47
D. 0.07
E. None of these

The table below gives the probabilities of combinations of religion and political parties in a major U.S. city.
What is the probability that a randomly selected person would be a Republican?
A.0.67
B. 0.22
C. 0.11
D. 0.39
E. None of these

Two events A and B are said to be mutually exclusive if:
A.P (A /B) = 1.
B. P (B /A) =1.
C. P (A and B) =1.
D. P (A and B) = 0.

If P(A) = 0.84, P(B) = 0.76 and P(A or B) = 0.90, then P(A and B) is:
A.0.06.
B. 0.14.
C. 0.70.
D. 0.83.

If P(A) = 0.25 and P(B) = 0.60, then P(A and B) is:
A.0.15.
B. 0.35.
C. 0.85.
D. Cannot be determined from the information given.

A basketball team at a university is composed of ten players. The team is made up of players who play either guard, forward, or center position. Four of the ten are guards; four of the ten are forwards; and two of the ten are centers. The numbers of the players are 1, 2, 3, 4, for the guards; 5, 6, 7, 8 for the forwards; and 9 and 10 for the centers. The starting five are numbered 1, 3, 5, 7, and 9. Let a player be selected at random from the ten. Define the following events:

A = player selected has a number from 1 to 8.

B = player selected is a guard.

C = player selected is a forward.

D = player selected is a starter.

E = player selected is a center.

P(A) is equal to:
A. 0.80.
B. 0.40.
C. 0.50.
D. 0.20.
E. 0.60.

A basketball team at a university is composed of ten players. The team is made up of players who play either guard, forward, or center position. Four of the ten are guards; four of the ten are forwards; and two of the ten are centers. The numbers of the players are 1, 2, 3, 4, for the guards; 5, 6, 7, 8 for the forwards; and 9 and 10 for the centers. The starting five are numbered 1, 3, 5, 7, and 9. Let a player be selected at random from the ten. Define the following events:

A = player selected has a number from 1 to 8.

B = player selected is a guard.

C = player selected is a forward.

D = player selected is a starter.

E = player selected is a center.

P(B) is equal to:
A. 0.80.
B. 0.40.
C. 0.50.
D. 0.20.
E. 0.30.

A basketball team at a university is composed of ten players. The team is made up of players who play either guard, forward, or center position. Four of the ten are guards; four of the ten are forwards; and two of the ten are centers. The numbers of the players are 1, 2, 3, 4, for the guards; 5, 6, 7, 8 for the forwards; and 9 and 10 for the centers. The starting five are numbered 1, 3, 5, 7, and 9. Let a player be selected at random from the ten. Define the following events:

A = player selected has a number from 1 to 8.

B = player selected is a guard.

C = player selected is a forward.

D = player selected is a starter.

E = player selected is a center.

P(D and E) is equal to:
A. 0.10.
B. 0.05.
C. 0.50.
D. 0.20.
E. 0.60.

A basketball team at a university is composed of ten players. The team is made up of players who play either guard, forward, or center position. Four of the ten are guards; four of the ten are forwards; and two of the ten are centers. The numbers of the players are 1, 2, 3, 4, for the guards; 5, 6, 7, 8 for the forwards; and 9 and 10 for the centers. The starting five are numbered 1, 3, 5, 7, and 9. Let a player be selected at random from the ten. Define the following events:

A = player selected has a number from 1 to 8.

B = player selected is a guard.

C = player selected is a forward.

D = player selected is a starter.

E = player selected is a center.

P(B and D) is equal to:
A. 0.80.
B. 0.40.
C. 0.50.
D. 0.20.
E. 0.30.

A basketball team at a university is composed of ten players. The team is made up of players who play either guard, forward, or center position. Four of the ten are guards; four of the ten are forwards; and two of the ten are centers. The numbers of the players are 1, 2, 3, 4, for the guards; 5, 6, 7, 8 for the forwards; and 9 and 10 for the centers. The starting five are numbered 1, 3, 5, 7, and 9. Let a player be selected at random from the ten. Define the following events:

A = player selected has a number from 1 to 8.

B = player selected is a guard.

C = player selected is a forward.

D = player selected is a starter.

E = player selected is a center.

P(B /D) is equal to:
A. 0.80.
B. 0.40.
C. 0.50.
D. 0.20.
E. 0.60.

A basketball team at a university is composed of ten players. The team is made up of players who play either guard, forward, or center position. Four of the ten are guards; four of the ten are forwards; and two of the ten are centers. The numbers of the players are 1, 2, 3, 4, for the guards; 5, 6, 7, 8 for the forwards; and 9 and 10 for the centers. The starting five are numbered 1, 3, 5, 7, and 9. Let a player be selected at random from the ten. Define the following events:

A = player selected has a number from 1 to 8.

B = player selected is a guard.

C = player selected is a forward.

D = player selected is a starter.

E = player selected is a center.

P(E /D) is equal to:
A. 0.80.
B. 0.40.
C. 0.50.
D. 0.20.
E. 0.10.

A useful graphical method of constructing the sample space for an experiment is:
A.tree diagram.
B. pie chart.
C. histogram.
D. bar graph.
E. scatter plot

Assume that A and B are independent events with P(A) = 0.40 and P(B) = 0.30. The probability that both events will occur simultaneously is:
A.0.10.
B. 0.12.
C. 0.70.
D. 0.75.
E. 1.0.

Two events A and B are said to be independent if:
A.P(A and B) = P(A) · P(B).
B. P(A and B) = P(A) + P(B).
C. P(A/B) = P(B).
D. P(B/A) = P(A).
E. P(A or B) = P(A) · P(B).

If A and B are independent events with P(A) = 0.25 and P(B) = 0.60, then P(A/B) is:
A.0.25.
B. 0.60.
C. 0.35.
D. 0.85.
E. 0.15

If the probability of drawing an Ace from a deck of cards is 0.077 and the probability of rolling a “2” using a fair die is 0.167, then the probability of drawing an Ace and rolling a “2” is
A.0.244
B. 0.090
C. 0.454
D. 0.013
E. 0.333

The joint probability of Events A and B is described as:
A.The probability of Event A, given that Event B has occurred.
B. The probability of Event B, given that Event A has occurred.
C. The probability that either Event A or Event B has occurred.
D. The probability that both Event A and Event B has occurred.

A survey revealed that 21.5% of the households had no checking account, 66.9% had regular checking accounts, and 11.6% had NOW accounts. Of those households with no checking account 40% had savings accounts. Of the households with regular checking accounts 71.6% had a savings account. Of the households with NOW accounts 79.3% had savings accounts.
The probability that a randomly selected household has a savings account is:
A.0.609.
B. 1.000.
C. 0.227.
D. 0.657.
E. 0.537.

A survey revealed that 21.5% of the households had no checking account, 66.9% had regular checking accounts, and 11.6% had NOW accounts. Of those households with no checking account 40% had savings accounts. Of the households with regular checking accounts 71.6% had a savings account. Of the households with NOW accounts 79.3% had savings accounts.
The probability that a randomly selected household has no checking account and no savings account is:
A.0.0860.
B. 0.1290.
C. 0.5330.
D. 0.1309.
E. 0.3430.

A survey revealed that 21.5% of the households had no checking account, 66.9% had regular checking accounts, and 11.6% had NOW accounts. Of those households with no checking account 40% had savings accounts. Of the households with regular checking accounts 71.6% had a savings account. Of the households with NOW accounts 79.3% had savings accounts.
The probability that a randomly selected household with a savings account has no checking account is:
A.0.1309.
B. 0.1290.
C. 0.1437.
D. 0.2150.
E. 0.4000.

Which of the following statements is correct given that the events A and B have nonzero probabilities?
A.A and B cannot be both independent and mutually exclusive
B. A and B can be both independent and mutually exclusive
C. A and B are always independent
D. A and B are always mutually exclusive

The odds of the Dallas Cowboys winning this year’s Super Bowl are 3 to 1. Compute the probability of the Cowboys winning.
0.75

The table below indicates the number of majors found in a college of business:
What is the probability that a randomly selected student is an accounting major?
0.129

The table below indicates the number of majors found in a college of business:
What is the probability that a randomly selected student is either a computer science major or a marketing major?
0.259

The table below indicates the number of majors found in a college of business:
What is the probability that a randomly selected student is a finance major and an accounting major?
0

An appliance dealer calculated the proportion of new dishwashers sold that required various numbers of service calls to correct problems during the warranty period. The records were:
Let X be the number of service calls during the warranty period for a dishwasher. What is the probability that there will be at least one service call but not more than 3?
0.72

An appliance dealer calculated the proportion of new dishwashers sold that required various numbers of service calls to correct problems during the warranty period. The records were:
Let X be the number of service calls during the warranty period for a dishwasher. What is the probability that there will be between two and four (inclusive) service calls?
0.37

An appliance dealer calculated the proportion of new dishwashers sold that required various numbers of service calls to correct problems during the warranty period. The records were:
Let X be the number of service calls during the warranty period for a dishwasher. What is the probability that there will be exactly one service call?
0.38

An appliance dealer calculated the proportion of new dishwashers sold that required various numbers of service calls to correct problems during the warranty period. The records were:
Let X be the number of service calls during the warranty period for a dishwasher. What is the probability that there will be at least one service call?
0.75

An appliance dealer calculated the proportion of new dishwashers sold that required various numbers of service calls to correct problems during the warranty period. The records were:
Let X be the number of service calls during the warranty period for a dishwasher. What is the probability that there will be at most one service call?
0.63

A personnel manager is reviewing number of overtime hours worked by employees in her plant. She has compiled the following data:
For a randomly selected employee let X be the number of overtime hours worked, and define the following events:

A = employee who works no overtime.

B = employee who works at least 7 hours overtime.

C = employee who works at most 4 hours overtime.

Determine the probability of event A.
0.128

A personnel manager is reviewing number of overtime hours worked by employees in her plant. She has compiled the following data:
For a randomly selected employee let X be the number of overtime hours worked, and define the following events:

A = employee who works no overtime.

B = employee who works at least 7 hours overtime.

C = employee who works at most 4 hours overtime.

Determine the probability of event B.
0.277

A personnel manager is reviewing number of overtime hours worked by employees in her plant. She has compiled the following data:
For a randomly selected employee let X be the number of overtime hours worked, and define the following events:

A = employee who works no overtime.

B = employee who works at least 7 hours overtime.

C = employee who works at most 4 hours overtime.

Determine the probability of event C.
0.425

The odds in favor of an event are the number of successes divided by the number of failures. The probability of this event occurring is the number of successes divided by the sum of the number of successes and the number of failures. The number of successes is five and the number of failures is four.
Find the probability of failure.
0.4444

A shoe store carries 590 pairs of Stacy-Adams and 610 pairs of Freeman brands of shoes. Let a success be the event of randomly selecting a pair of Stacy-Adams shoes.
Find the probability of a success.
0.4917

In the board game called TRIVIAL PURSUIT, a single die is used to determine the number of spaces a player is allowed to move. A player is currently positioned 3 spaces from a space where a correct answer will earn a “pie” and 4 spaces from a space where “roll again” is the option. Assuming a fair die, what is the probability the player will get to answer a question for a “pie” or get to “roll again”?
0.333

Find P (C1 and D1).
0.075

Find P (D1) or P (C1).
0.60

Find P (C1 or D1).
0.525

Find P (D1 or D2 or D3).
1.00

Six candidates for a new position of vice-president for academic affairs have been selected. Three of the candidates are female. The candidates’ years of experience are as follows:
Suppose one of the candidates is selected at random. Define the following events:

A = person selected has 9 years experience.

B = person selected is a female.

Find P(A).
0.167

Six candidates for a new position of vice-president for academic affairs have been selected. Three of the candidates are female. The candidates’ years of experience are as follows:
Suppose one of the candidates is selected at random. Define the following events:

A = person selected has 9 years experience.

B = person selected is a female.

Find P(B).
0.500

Six candidates for a new position of vice-president for academic affairs have been selected. Three of the candidates are female. The candidates’ years of experience are as follows:
Suppose one of the candidates is selected at random. Define the following events:

A = person selected has 9 years experience.

B = person selected is a female.

Find P(A / B).
0.333

Six candidates for a new position of vice-president for academic affairs have been selected. Three of the candidates are female. The candidates’ years of experience are as follows:
Suppose one of the candidates is selected at random. Define the following events:

A = person selected has 9 years experience.

B = person selected is a female.

Find P(not A / B).
0.667

A large men’s store in a mall purchases suits from four different manufacturers in short, regular, and long. Their current selections are given in the contingency table below:
Let the abbreviations and letters represent the events. For example Event S = a randomly selected suit is short, event HMS = a randomly selected suit is manufactured by HMS.

Compute P(S).
0.20

A large men’s store in a mall purchases suits from four different manufacturers in short, regular, and long. Their current selections are given in the contingency table below:
Let the abbreviations and letters represent the events. For example Event S = a randomly selected suit is short, event HMS = a randomly selected suit is manufactured by HMS.

Compute P(HMS).
0.20

A large men’s store in a mall purchases suits from four different manufacturers in short, regular, and long. Their current selections are given in the contingency table below:
Let the abbreviations and letters represent the events. For example Event S = a randomly selected suit is short, event HMS = a randomly selected suit is manufactured by HMS.

Compute P(S and HMS).
0.03

A large men’s store in a mall purchases suits from four different manufacturers in short, regular, and long. Their current selections are given in the contingency table below:
Let the abbreviations and letters represent the events. For example Event S = a randomly selected suit is short, event HMS = a randomly selected suit is manufactured by HMS.

Compute P(S /HMS).
0.15

A large men’s store in a mall purchases suits from four different manufacturers in short, regular, and long. Their current selections are given in the contingency table below:
Let the abbreviations and letters represent the events. For example Event S = a randomly selected suit is short, event HMS = a randomly selected suit is manufactured by HMS.

Compute P(HMS / S).
0.15

A political telephone survey of 360 people asked whether they were in favor or not in favor of a proposed law. Each person was identified as either Republican or Democrat. The results are shown in the following table:

Party	In Favor	Not in Favor	Undecided	Total
Republican	98	54	40	192
Democrat	79	29	60	168
Total	177	83	100	360

What is the probability that a randomly selected respondent was in favor of the proposed law?
0.492

A political telephone survey of 360 people asked whether they were in favor or not in favor of a proposed law. Each person was identified as either Republican or Democrat. The results are shown in the following table:

Party	In Favor	Not in Favor	Undecided	Total
Republican	98	54	40	192
Democrat	79	29	60	168
Total	177	83	100	360

What is the probability that a randomly selected respondent was a Democrat?
0.467

A political telephone survey of 360 people asked whether they were in favor or not in favor of a proposed law. Each person was identified as either Republican or Democrat. The results are shown in the following table:

Party	In Favor	Not in Favor	Undecided	Total
Republican	98	54	40	192
Democrat	79	29	60	168
Total	177	83	100	360

What is the probability that a randomly selected respondent was a Republican and undecided about the proposed law?
0.111

A political telephone survey of 360 people asked whether they were in favor or not in favor of a proposed law. Each person was identified as either Republican or Democrat. The results are shown in the following table:

Party	In Favor	Not in Favor	Undecided	Total
Republican	98	54	40	192
Democrat	79	29	60	168
Total	177	83	100	360

What is the probability that a randomly selected respondent was a Democrat or not in favor of the proposed law?
0.617

A political telephone survey of 360 people asked whether they were in favor or not in favor of a proposed law. Each person was identified as either Republican or Democrat. The results are shown in the following table:

Party	In Favor	Not in Favor	Undecided	Total
Republican	98	54	40	192
Democrat	79	29	60	168
Total	177	83	100	360

Given that the respondent was in favor of the proposed law, what is the probability that they were a Republican?
0.554

A Gulf Coast travel park has the following accommodations:

Number of Bedrooms
Location	3 Bedroom	4 Bedroom	Total
Beach Front	17	24	41
Non Beach Front	6	210	216
Total	23	234	257

What is the probability of selecting a beachfront site?
0.1595

A Gulf Coast travel park has the following accommodations:

Number of Bedrooms
Location	3 Bedroom	4 Bedroom	Total
Beach Front	17	24	41
Non Beach Front	6	210	216
Total	23	234	257

What is the probability of selecting a non beach front site with 3 bedrooms?
0.023

A Gulf Coast travel park has the following accommodations:

Number of Bedrooms
Location	3 Bedroom	4 Bedroom	Total
Beach Front	17	24	41
Non Beach Front	6	210	216
Total	23	234	257

What is the probability of selecting a non beach front site given that the facility had 4 bedrooms?
0.897

The physical science degrees conferred by a school between 1992 and 1995 were broken down as follows:
Suppose a person is selected at random from these graduates. Consider the following events:

M: The person is a male.

F: The person is a female.

P: The person graduated in physics.

C: The person graduated in chemistry.

G: The person graduated in geology.

Find P(M).
0.575

The physical science degrees conferred by a school between 1992 and 1995 were broken down as follows:
Suppose a person is selected at random from these graduates. Consider the following events:

M: The person is a male.

F: The person is a female.

P: The person graduated in physics.

C: The person graduated in chemistry.

G: The person graduated in geology.

Find P(M / P).
0.500

The physical science degrees conferred by a school between 1992 and 1995 were broken down as follows:
Suppose a person is selected at random from these graduates. Consider the following events:

M: The person is a male.

F: The person is a female.

P: The person graduated in physics.

C: The person graduated in chemistry.

G: The person graduated in geology.

Find P(M and P).
0.125

The physical science degrees conferred by a school between 1992 and 1995 were broken down as follows:
Suppose a person is selected at random from these graduates. Consider the following events:

M: The person is a male.

F: The person is a female.

P: The person graduated in physics.

C: The person graduated in chemistry.

G: The person graduated in geology.

Find P(C / F).
0.47

A study of Brand D washing machines that failed within three years (warranty period) was 23.2%. Of those that failed, 82.9% lasted over two years. What is the probability that a washer, which lasts at least two years, will still fail before the end of the warranty period?
0.171

A firm produces three qualities of bed linens — good, better, best. Production is scheduled to result in 50% good, 35% better, and 15% best. A quality control person checks the finished product and classified them as acceptable or imperfect. The percentages acceptable are good, 92%; better, 88%; best, 82%. Find the posterior probability that a sheet, which is “acceptable”, will be acceptable.
0.1380

The prior probabilities for two events A₁ and A₂ are P(A₁) = .30 and P(A₂) = .70. It is also known that P(A₁ and A₂) = 0. Suppose P(B / A₁) = .15 and P(B / A₂) = .05.
Compute P(A₁ and B).
0.045

The prior probabilities for two events A₁ and A₂ are P(A₁) = .30 and P(A₂) = .70. It is also known that P(A₁ and A₂) = 0. Suppose P(B / A₁) = .15 and P(B / A₂) = .05.
Compute P(A₂ and B).
0.035

The prior probabilities for two events A₁ and A₂ are P(A₁) = .30 and P(A₂) = .70. It is also known that P(A₁ and A₂) = 0. Suppose P(B / A₁) = .15 and P(B / A₂) = .05.
Compute P(B).
0.08

The prior probabilities for two events A₁ and A₂ are P(A₁) = .30 and P(A₂) = .70. It is also known that P(A₁ and A₂) = 0. Suppose P(B / A₁) = .15 and P(B / A₂) = .05.
Apply Bayes’ theorem to compute P(A₁ / B).
0.5625

The prior probabilities for two events A₁ and A₂ are P(A₁) = .30 and P(A₂) = .70. It is also known that P(A₁ and A₂) = 0. Suppose P(B / A₁) = .15 and P(B / A₂) = .05.
Apply Bayes’ theorem to compute P(A₂ / B).
0.4375

The prior probabilities of events A₁, A₂, and A₃ are P(A₁) = .50, P(A₂) = .20 and P(A₃) = .30. The conditional probabilities of event B given A₁, A₂, and A₃ are P(B / A₁) = .40, P(B / A₂) = .50 and P(B / A₃) = .30.
Compute P(B and A₁).
0.20

The prior probabilities of events A₁, A₂, and A₃ are P(A₁) = .50, P(A₂) = .20 and P(A₃) = .30. The conditional probabilities of event B given A₁, A₂, and A₃ are P(B / A₁) = .40, P(B / A₂) = .50 and P(B / A₃) = .30.
Compute P(B and A₂).
0.10

The prior probabilities of events A₁, A₂, and A₃ are P(A₁) = .50, P(A₂) = .20 and P(A₃) = .30. The conditional probabilities of event B given A₁, A₂, and A₃ are P(B / A₁) = .40, P(B / A₂) = .50 and P(B / A₃) = .30.
Compute P(B and A₃).
0.09

The prior probabilities of events A₁, A₂, and A₃ are P(A₁) = .50, P(A₂) = .20 and P(A₃) = .30. The conditional probabilities of event B given A₁, A₂, and A₃ are P(B / A₁) = .40, P(B / A₂) = .50 and P(B / A₃) = .30.
Compute P(B).
0.39

The prior probabilities of events A₁, A₂, and A₃ are P(A₁) = .50, P(A₂) = .20 and P(A₃) = .30. The conditional probabilities of event B given A₁, A₂, and A₃ are P(B / A₁) = .40, P(B / A₂) = .50 and P(B / A₃) = .30.
Apply Bayes’ theorem to compute the posterior probability P(A₁ / B).
0.5128

The prior probabilities of events A₁, A₂, and A₃ are P(A₁) = .50, P(A₂) = .20 and P(A₃) = .30. The conditional probabilities of event B given A₁, A₂, and A₃ are P(B / A₁) = .40, P(B / A₂) = .50 and P(B / A₃) = .30.
Apply Bayes’ theorem to compute the posterior probability P(A₂ / B).
0.2564

The prior probabilities of events A₁, A₂, and A₃ are P(A₁) = .50, P(A₂) = .20 and P(A₃) = .30. The conditional probabilities of event B given A₁, A₂, and A₃ are P(B / A₁) = .40, P(B / A₂) = .50 and P(B / A₃) = .30.
Apply Bayes’ theorem to compute the posterior probability P(A₃ / B).
0.2308

An investment counselor would like to meet with 14 of his clients on Wednesday, but he only has time for 10 appointments. How many different combinations of the clients could be considered for inclusion into his limited schedule for that day?
1001

How many different combinations are possible if 8 substitute workers are available to fill 4 openings created by employees planning to take vacation leave next week?
70

Ten students from an economics class have formed a study group. Each may or may not attend a study session. Assuming that the members will be making independent decisions on whether or not to attend, how many different possibilities exist for the composition of the study session?
1024

A state’s license plate has 9 positions, each of which has 37 possibilities (26 letters, 10 integers, or blank). If the purchaser of a vanity plate wants his first seven positions to be Stanley, in how many ways can his plate appear?
1369

The following represent interest rates on 20 U.S. Treasury bond issues with maturity dates in 2000-2001, as listed in Money Magazine:
Determine the probability that a randomly selected bond will have a rate of interest between 11 and 12 percent.
0.35

The following represent interest rates on 20 U.S. Treasury bond issues with maturity dates in 2000-2001, as listed in Money Magazine:
Determine the probability that a randomly selected bond will have a rate of interest of ten percent up to but not including 14 percent.
0.75

The following represent interest rates on 20 U.S. Treasury bond issues with maturity dates in 2000-2001, as listed in Money Magazine:
Determine the probability that a randomly selected bond will have a rate of interest of at least 14 percent, but less than 15 percent.
0.15

The following represent interest rates on 20 U.S. Treasury bond issues with maturity dates in 2000-2001, as listed in Money Magazine:
Determine the probability that a randomly selected bond will have a rate of interest of less than 13 percent.
0.75

The following represent interest rates on 20 U.S. Treasury bond issues with maturity dates in 2000-2001, as listed in Money Magazine:
Determine the probability that a randomly selected bond will have a rate of interest of 11 percent or more.
0.75

The following represent interest rates on 20 U.S. Treasury bond issues with maturity dates in 2000-2001, as listed in Money Magazine:
Using the letter identifications, calculate P (A or F).
0.25

The following represent interest rates on 20 U.S. Treasury bond issues with maturity dates in 2000-2001, as listed in Money Magazine:
Using the letter identifications, calculate P (B and D).
0.00

The Burger Queen Company has 124 locations along the west coast. The general manager is concerned with the profitability of the locations compared with major menu items sold. The information below shows the number of each menu item selected by profitability of store.
If a menu item is selected at random, what is the probability that the store is a high profit store?
0.414

The Burger Queen Company has 124 locations along the west coast. The general manager is concerned with the profitability of the locations compared with major menu items sold. The information below shows the number of each menu item selected by profitability of store.
What is the probability that an item selected at random is a Mother burger?
0.218

The Burger Queen Company has 124 locations along the west coast. The general manager is concerned with the profitability of the locations compared with major menu items sold. The information below shows the number of each menu item selected by profitability of store.
What is the probability of selecting a menu item from a high profit store and it is nachos?
0.174

The Burger Queen Company has 124 locations along the west coast. The general manager is concerned with the profitability of the locations compared with major menu items sold. The information below shows the number of each menu item selected by profitability of store.
What is the probability of tacos being selected at a low profit store?
0.197

Intentions of consumers regarding future automobile purchases and the financial capability of the consumers are given below:
For a randomly selected consumer, find the following probability: P(D).
0.6

Intentions of consumers regarding future automobile purchases and the financial capability of the consumers are given below:
For a randomly selected consumer, find the following probability: P(B and D).
0.2

Intentions of consumers regarding future automobile purchases and the financial capability of the consumers are given below:
For a randomly selected consumer, find the following probability: P(A and D).
0.3

Intentions of consumers regarding future automobile purchases and the financial capability of the consumers are given below:
For a randomly selected consumer, find the following probability: P(A or D).
0.7

Intentions of consumers regarding future automobile purchases and the financial capability of the consumers are given below:
For a randomly selected consumer, find the following probability: P(A / D).
0.5

Intentions of consumers regarding future automobile purchases and the financial capability of the consumers are given below:
For a randomly selected consumer, find the following probability: P(E / B).
0.33

A dormitory has two activating devices in each fire detector. One is smoke activated and has a probability of .98 of sounding an alarm when it should. The second is a heat sensitive activator and has a probability of .95 of operating when it should. Each activator operates independently of the other. Presume a fire starts near a detector.
What is the probability that the detector will sound an alarm?
0.999

A dormitory has two activating devices in each fire detector. One is smoke activated and has a probability of .98 of sounding an alarm when it should. The second is a heat sensitive activator and has a probability of .95 of operating when it should. Each activator operates independently of the other. Presume a fire starts near a detector.
What is the probability that both types of activators will work properly?
0.931

A dormitory has two activating devices in each fire detector. One is smoke activated and has a probability of .98 of sounding an alarm when it should. The second is a heat sensitive activator and has a probability of .95 of operating when it should. Each activator operates independently of the other. Presume a fire starts near a detector.
What is the probability that only the smoke activator functions?
0.049

____________________ probabilities find their greatest application in games of chance, but they are not so useful when the underlying processes are not well known.
Classical

Because we can determine the probability without actually engaging in any experiments, the classical approach is also referred to as the ____________________ approach.
a priori

The relative frequency approach to probability depends on the law of ______________________________.
large numbers

Probability refers to a number between ____________________ and ____________________ which expresses the ____________________ that an event will occur.
zero; one; chanceor
0, 1, chance

You have applied for a job and are told by the interviewer that the probability of your being hired is 0.70. Calculate the odds that you will be hired.
The odds are ____________________ to ____________________.
7: 3or
seven; three

The probability of a tornado hitting in your city has been estimated at 0.001. What are the corresponding odds?
The odds are ____________________ to ____________________.
1; 999

In a state lottery, which pays at least one million dollars, six numbers from 1 to 50 are randomly selected. If five have been selected and your ticket matches the first five, what are the odds that the sixth number will make you a millionaire?
The odds are ____________________ to ____________________.
1; 44

The grade distribution for a particular statistics exam was recorded as follows:

Grade	Number of Students
90-100	10
80-89	10
70-79	8
60-69	2
Total	30

An event A and its complement A‘ are always ___________________________________.
mutually exclusive

A set of events is ____________________ if it includes all the possible outcomes of an experiment.
exhaustive

The ____________________ of events describes the case where two or more events occur at the same time.
intersection

When we wish to determine the probability that one or more of several events will occur in an experiment, we would use ____________________ rules.
addition

When events are ____________________ the occurrence of one means that none of the others can occur.
mutually exclusive

Events are ____________________ when the occurrence of one event has no effect on the probability that another will occur.
independent

Events are ____________________ when the occurrence of one event changes the probability that another will occur.
dependent

The physical science degrees conferred by a school between 1992 and 1995 were broken down as follows:
Suppose a person is selected at random from these graduates. Consider the following events:

M: The person is a male.

F: The person is a female.

P: The person graduated in physics.

C: The person graduated in chemistry.

G: The person graduated in geology.

Complete the formula: P(M / P) = P(P and M) / ____________________.
P(P)

____________________ refer to the number of different ways in which objects can be arranged in order.
Permutations

____________________ consider only the possible sets of objects, regardless of the order in which the members of the set are arranged.
Combinations

The odds in favor of an event are the number of successes divided by the number of failures. The probability of this event occurring is the number of successes divided by the sum of the number of successes and the number of failures. The number of successes is five and the number of failures is four.
Find the odds in favor of success.

The odds are ____________________ to ____________________.
5; 4 or
five, four

A shoe store carries 590 pairs of Stacy-Adams and 610 pairs of Freeman brands of shoes. Let a success be the event of randomly selecting a pair of Stacy-Adams shoes.
Find the odds of selecting a pair of Stacy-Adams shoes.

The odds are ____________________ to ____________________.
590; 610

If the odds in favor of an event happening are A:B, what is the probability being expressed?

You think you have a 95% chance of passing your next business statistics exam. This is an example of which approach to probability?

Subjective

Create a Venn diagram illustrating an Event A, and its complement.

From an ordinary deck of 52 playing cards one is selected at random. Define the following events:
A = card selected is an Ace.

B = card selected is a Queen.

C = card selected is a three.

Are A, B, and C mutually exclusive events?

Use the addition rule to find P(A or B or C).

Yes; 0.2308

According to an old song lyric, “love and marriage go together like a horse and carriage.” Let love be event A and marriage be event B. Are events A and B mutually exclusive?

One card is randomly selected from a deck of 52 playing cards. Define the following events:
A = card selected is a five.

B = card selected is a ten.

C = card selected is a jack.

Find P(not A or not B or not C) using the addition rule.

1 – [(4/52) + (4/52) + (4/52)] = 0.7692

Six candidates for a new position of vice-president for academic affairs have been selected. Three of the candidates are female. The candidates’ years of experience are as follows:
Suppose one of the candidates is selected at random. Define the following events:

A = person selected has 9 years experience.

B = person selected is a female.

Are events A and B independent? Explain using probability.

No; P(A/B) is not equal to P(A).

A Gulf Coast travel park has the following accommodations:

Number of Bedrooms
Location	3 Bedroom	4 Bedroom	Total
Beach Front	17	24	41
Non Beach Front	6	210	216
Total	23	234	257

Is the event of selecting a beach front site independent of the event of selecting a 3 bedroom facility? Explain.

No; P(beach front) = .1595; P(3 bedroom) = .0895 P(beach front/3 bedroom) = .7391 Since 0.1595 is not equal to 0.7391 or 0.0895 is not equal to 0.7391, these events are not independent events.

The physical science degrees conferred by a school between 1992 and 1995 were broken down as follows:
Suppose a person is selected at random from these graduates. Consider the following events:

M: The person is a male.

F: The person is a female.

P: The person graduated in physics.

C: The person graduated in chemistry.

G: The person graduated in geology.

Are the events C and F independent?

The physical science degrees conferred by a school between 1992 and 1995 were broken down as follows:
Suppose a person is selected at random from these graduates. Consider the following events:

M: The person is a male.

F: The person is a female.

P: The person graduated in physics.

C: The person graduated in chemistry.

G: The person graduated in geology.

Explain why events C and F are or are not independent.

P(C/F) = 0.47 and P(C) = 0.5, so P(C/F) is not equal to P(C)

The prior probabilities for two events A₁ and A₂ are P(A₁) = .30 and P(A₂) = .70. It is also known that P(A₁ and A₂) = 0. Suppose P(B / A₁) = .15 and P(B / A₂) = .05.
Are A₁ and A₂ mutually exclusive? Explain.

Yes; Yes, since P(A₁ and A₂) = 0.

Machine A produces 3% defectives, machine B produces 5% defectives, and machine C produces 10% defectives. Of the total output from these machines, 60% of the items are from machine A, 30% from B, and 10% from C. One item is selected at random from a day’s production.
What is the prior probability that the item came from machine A?

Machine B?

Machine C?

P(A) = 0.60; P(B) = 0.30; P(C) = 0.10

Machine A produces 3% defectives, machine B produces 5% defectives, and machine C produces 10% defectives. Of the total output from these machines, 60% of the items are from machine A, 30% from B, and 10% from C. One item is selected at random from a day’s production.
What is the probability that the item is defective?

P(D) = P(A)P(D|A) + P(B)P(D|B) + P(C)P(D|C)
= (.60)(.03) + (.30)(.05) + (.10)(.10) = 0.043

Machine A produces 3% defectives, machine B produces 5% defectives, and machine C produces 10% defectives. Of the total output from these machines, 60% of the items are from machine A, 30% from B, and 10% from C. One item is selected at random from a day’s production.
If inspection finds the item to be defective, what is the revised probability that the item came from machine C?

Machine A produces 3% defectives, machine B produces 5% defectives, and machine C produces 10% defectives. Of the total output from these machines, 60% of the items are from machine A, 30% from B, and 10% from C. One item is selected at random from a day’s production.
If inspection finds the item to be defective, what is the revised probability that the item came from machine B?

Machine A produces 3% defectives, machine B produces 5% defectives, and machine C produces 10% defectives. Of the total output from these machines, 60% of the items are from machine A, 30% from B, and 10% from C. One item is selected at random from a day’s production.
If inspection finds the item to be defective, what is the revised probability that the item came from machine A?

I would like to select 3 paperback books from a list of 12 books to take on vacation. How many different sets of 3 books can I choose?

12 C 3 = 220

At a track meet, eight runners are competing in the 100-yard dash. First, second, and third trophies will be awarded. In how many ways can the trophies be awarded?

(8!/5!) = 336

In advertising a mountain cabin near Keystone, Colorado, a property owner can specify (1) whether or not pets are permitted, (2) whether the rent is based on off-season, during summer season, or during the Dec.-Jan. peak skiing season, (3) whether or not children under 12 are allowed, and (4) whether the minimum stay is for 4, 7, or 10 days. How many different versions of the ad can be generated?

The Burger Queen Company has 124 locations along the west coast. The general manager is concerned with the profitability of the locations compared with major menu items sold. The information below shows the number of each menu item selected by profitability of store.
If a menu order is selected at random, describe the following in words.

A) P(M5)

B) P(R3)

C) P(R2 and M3)

D) P(M2 / R2)

E) P(R1 / M4)

Probability of tacos being ordered.; Probability of a store being a Low Profit Store.; Probability that a Father Burger is ordered at a Medium Profit Store.; Probability of a Mother Burger being ordered knowing it was at a Medium Profit Store.; Probability that the store is High Profit given Nachos are ordered.

The Burger Queen Company has 124 locations along the west coast. The general manager is concerned with the profitability of the locations compared with major menu items sold. The information below shows the number of each menu item selected by profitability of store.
Is the sale of Mother Burgers independent of profitability of store?

The Burger Queen Company has 124 locations along the west coast. The general manager is concerned with the profitability of the locations compared with major menu items sold. The information below shows the number of each menu item selected by profitability of store.
What item was the favorite in a medium profit store?

What percentage of the time was this item selected?

Father Burger; 27.1%

The Burger Queen Company has 124 locations along the west coast. The general manager is concerned with the profitability of the locations compared with major menu items sold. The information below shows the number of each menu item selected by profitability of store.
What item was selected the least at any type store?

What percentage of the time was this item selected?

Tacos; 15.2%

The Burger Queen Company has 124 locations along the west coast. The general manager is concerned with the profitability of the locations compared with major menu items sold. The information below shows the number of each menu item selected by profitability of store.
What item has the highest probability of being selected for any type store?

What percentage of the time was this item selected?

Father Burger; 27.6%

The Burger Queen Company has 124 locations along the west coast. The general manager is concerned with the profitability of the locations compared with major menu items sold. The information below shows the number of each menu item selected by profitability of store.
Determine the probability for:

A) P(M5)

B) P(R3)

C) P(R2 and M3)

D) P(M2 / R2)

E) P(R1 / M4)

0.152; 0.254; 0.090; 0.234; 0.410

An investment firm has classified its clients according to their gender and the composition of their investment portfolio (primarily bonds, primarily stocks, or a balanced mix of bonds and stocks). The proportions of clients falling into the various categories are shown in the following table:

Portfolio Composition
Gender	Bonds	Stocks	Balanced
Male	0.18	0.20	0.25
Female	0.12	0.05	0.20

One client is selected at random, and two events A and B are defined as follows:

A: The client selected is male.

B: The client selected has a balanced portfolio.

Express each of the following events in words:

A) A or B

B) A and B

C) A and

D) or

The client selected either is male or has a balanced portfolio or both.; The client selected is male and has a balanced portfolio.; The client selected is male and has an unbalanced portfolio.; The client selected either is female or has an unbalanced portfolio or both.

An investment firm has classified its clients according to their gender and the composition of their investment portfolio (primarily bonds, primarily stocks, or a balanced mix of bonds and stocks). The proportions of clients falling into the various categories are shown in the following table:

Portfolio Composition
Gender	Bonds	Stocks	Balanced
Male	0.18	0.20	0.25
Female	0.12	0.05	0.20

One client is selected at random, and two events A and B are defined as follows:

A: The client selected is male.

B: The client selected has a balanced portfolio.

Find the following probabilities:

A) P(A)

B) P(B)

0.63; 0.45

An investment firm has classified its clients according to their gender and the composition of their investment portfolio (primarily bonds, primarily stocks, or a balanced mix of bonds and stocks). The proportions of clients falling into the various categories are shown in the following table:

Portfolio Composition
Gender	Bonds	Stocks	Balanced
Male	0.18	0.20	0.25
Female	0.12	0.05	0.20

One client is selected at random, and two events A and B are defined as follows:

A: The client selected is male.

B: The client selected has a balanced portfolio.

Find the following probabilities:

A) P(A or B)

B) P(A and B)

0.83; 0.25

An investment firm has classified its clients according to their gender and the composition of their investment portfolio (primarily bonds, primarily stocks, or a balanced mix of bonds and stocks). The proportions of clients falling into the various categories are shown in the following table:

Portfolio Composition
Gender	Bonds	Stocks	Balanced
Male	0.18	0.20	0.25
Female	0.12	0.05	0.20

One client is selected at random, and two events A and B are defined as follows:

A: The client selected is male.

B: The client selected has a balanced portfolio.

Express each of the following probabilities in words:

A) P(A/B)

B) P(B/A)

The probability that the employee selected is male, given that the employee has a balanced portfolio.; The probability that the employee selected has a balanced portfolio, given that the employee is male.

An investment firm has classified its clients according to their gender and the composition of their investment portfolio (primarily bonds, primarily stocks, or a balanced mix of bonds and stocks). The proportions of clients falling into the various categories are shown in the following table:

Portfolio Composition
Gender	Bonds	Stocks	Balanced
Male	0.18	0.20	0.25
Female	0.12	0.05	0.20

One client is selected at random, and two events A and B are defined as follows:

A: The client selected is male.

B: The client selected has a balanced portfolio.

Find the following probabilities:

A) P(A/B)

B) P(B/A)

0.555; 0.397

An investment firm has classified its clients according to their gender and the composition of their investment portfolio (primarily bonds, primarily stocks, or a balanced mix of bonds and stocks). The proportions of clients falling into the various categories are shown in the following table:

Portfolio Composition
Gender	Bonds	Stocks	Balanced
Male	0.18	0.20	0.25
Female	0.12	0.05	0.20

One client is selected at random, and two events A and B are defined as follows:

A: The client selected is male.

B: The client selected has a balanced portfolio.

Are A and B independent events? Explain.

No; P(A / B) = 0.555 is not equal to P(A) = 0.63

An investment firm has classified its clients according to their gender and the composition of their investment portfolio (primarily bonds, primarily stocks, or a balanced mix of bonds and stocks). The proportions of clients falling into the various categories are shown in the following table:

Portfolio Composition
Gender	Bonds	Stocks	Balanced
Male	0.18	0.20	0.25
Female	0.12	0.05	0.20

One client is selected at random, and two events A and B are defined as follows:

A: The client selected is male.

B: The client selected has a balanced portfolio.

Are A and B mutually exclusive events? Explain.

No. Since it’s possible to be both a male and have a balanced fund, P(A and B) = 0.25 which is not equal to zero.

There are 12 players on a basketball team and 5 of those players start the game. How many different starting lineups are possible?

12 C 5 = 792

What is the subjective approach to probability?

The degree to which one happens to believe that an event will or will not happen.

Explain the relationship between a relative-frequency distribution and a probability distribution for any numerical population.

A relative frequency distribution indicates the decimal fraction that each class contains of the total number of pieces of data. Let one of the classes be defined as the random variable X. Then the probability of X will be the relative frequency of the class representing X.

Identify the following type of graphic, and describe what it illustrates:

Venn diagram illustrates the intersection of two events, when two or more events occur at the same time.

Define contingency table.

Cross-classification array taking into account all the different possibilities in the array.

Define marginal probability.

Marginal probability is the probability that a given event will occur, with no other events taken into consideration. In a contingency table, marginal probabilities are computed by dividing the row and column totals by the sum of the frequencies.

Define conditional probability.

The probability that an event will occur, given that another event has already occurred.

Write a word statement for P (B / A).

The probability that event B will occur given that event A has already occurred.

State in your own words the probability concept of independence.

The probability of two events is unaltered whether or not one of them has happened.

Express the probability concept of independence for events A and B in marginal and conditional probabilities.

P(A / B) = P(A) or P(B /A) = P(B).

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