Statistical Techniques in Business And Economics 15th Edition By Lind - Test Bank

Statistical Techniques in Business And Economics 15th Edition By Lind – Test Bank

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Chapter 05

A Survey of Probability Concepts

True / False Questions

The probability of rolling a 3 or 2 on a single die is an example of conditional probability.
True False

The probability of rolling a 3 or 2 on a single die is an example of mutually exclusive events.
True False

An individual can assign a subjective probability to an event based on the individual’s knowledge about the event.
True False

To apply the special rule of addition, the events must be mutually exclusive.
True False

A joint probability measures the likelihood that two or more events will happen concurrently.
True False

The joint probability of two independent events, A and B, is computed as: P(A and B) = P(A) P(B).
True False

The joint probability of two events, A and B, that are not independent is computed as: P(A and B) = P(A) P(B|A).
True False

A coin is tossed four times. The joint probability that all four tosses will result in a head is ¼ or 0.25.
True False

If there are ‘m’ ways of doing one thing and ‘n’ ways of doing another thing, the multiplication formula states that there are (m) · (n) ways of doing both.
True False

A combination of a set of objects is defined by the order of the objects.
True False

The complement rule states that the probability of an event not occurring is equal to one minus the probability of its occurrence.
True False

If two events are mutually exclusive, then P(A or B) = P(A) P(B).
True False

An illustration of an experiment is turning the ignition key of an automobile as it comes off the assembly line to determine whether or not the engine will start.
True False

Bayes’ theorem is a method to revise the probability of an event given additional information.
True False

Bayes’ theorem is used to calculate a subjective probability.
True False

Multiple Choice Questions

The National Center for Health Statistics reported that of every 883 deaths in recent years, 24 resulted from an automobile accident, 182 from cancer and 333 from heart disease. What is the probability that a particular death is due to an automobile accident?
A. 24/883 or 0.027
B. 539/883 or 0.610
C. 24/333 or 0.072
D. 182/883 or 0.206

If two events A and B are mutually exclusive, what does the special rule of addition state?
A. P(A or B) = P(A) + P(B)
B. P(A and B) = P(A) + P(B)
C. P(A and/or B) = P(A) + P(B)
D. P(A or B) = P(A) – P(B)

What does the complement rule state?
A. P(A) = P(A) – P(B)
B. P(A) = 1 – P(not A)
C. P(A) = P(A) · P(B)
D. P(A) = P(A)X + P(B)

Which approach to probability is exemplified by the following formula?
Probability of an Event =

A. Classical approach
B. Empirical approach
C. Subjective approach
D. None of the above

A study of 200 computer service firms revealed these incomes after taxes:
What is the probability that a particular firm selected has $1 million or more in income after taxes?
A. 0.00
B. 0.25
C. 0.49
D. 0.51

A firm offers routine physical examinations as part of a health service program for its employees. The exams showed that 8% of the employees needed corrective shoes, 15% needed major dental work and 3% needed both corrective shoes and major dental work. What is the probability that an employee selected at random will need either corrective shoes or major dental work?
A. 0.20
B. 0.25
C. 0.50
D. 1.00

A survey of top executives revealed that 35% of them regularly read Time magazine, 20% read Newsweek and 40% read U.S. News & World Report. Ten percent read both Time and U.S. News & World Report. What is the probability that a particular top executive reads either Time or U.S. News & World Report regularly?
A. 0.85
B. 0.06
C. 1.00
D. 0.65

A study by the National Park Service revealed that 50% of the vacationers going to the Rocky Mountain region visit Yellowstone Park, 40% visit the Grand Tetons and 35% visit both. What is the probability that a vacationer will visit at least one of these magnificent attractions?
A. 0.95
B. 0.35
C. 0.55
D. 0.05

A tire manufacturer advertises, “the median life of our new all-season radial tire is 50,000 miles. An immediate adjustment will be made on any tire that does not last 50,000 miles.” You purchased four of these tires. What is the probability that all four tires will wear out before traveling 50,000 miles?
A. 1/10 or 0.10
B. ¼ or 0.25
C. 1/64 or 0.0156
D. 1/16 or 0.0625

A sales representative calls on four hospitals in Westchester County. It is immaterial what order he calls on them. How many ways can he organize his calls?
A. 4
B. 24
C. 120
D. 37

There are 10 rolls of film in a box and 3 are defective. Two rolls are selected without replacement. What is the probability of selecting a defective roll followed by another defective roll?
A. ½ or 0.50
B. ¼ or 0.25
C. 1/120 or about 0.0083
D. 1/15 or about 0.07

Giorgio offers the person who purchases an 8 ounce bottle of Allure two free gifts, either an umbrella, a 1 ounce bottle of Midnight, a feminine shaving kit, a raincoat or a pair of rain boots. If you purchased Allure what is the probability you randomly selected an umbrella and a shaving kit in that order?
A. 0.00
B. 1.00
C. 0.05
D. 0.20

A board of directors consists of eight men and four women. A four-member search committee is randomly chosen to recommend a new company president. What is the probability that all four members of the search committee will be women?
A. 1/120 or 0.00083
B. 1/16 or 0.0625
C. ⅛ or 0.125
D. 1/495 or 0.002

A lamp manufacturer has developed five lamp bases and four lampshades that could be used together. How many different arrangements of base and shade can be offered?
A. 5
B. 10
C. 15
D. 20

A gumball machine has just been filled with 50 black, 150 white, 100 red and 100 yellow gum balls that have been thoroughly mixed. Sue and Jim, each, purchased one gumball. What is the likelihood both Sue and Jim get red gumballs?
A. 0.50
B. 0.062
C. 0.33
D. 0.75

What does equal?
A. 640
B. 36
C. 10
D. 120

In a management trainee program, 80 percent of the trainees are female, 20 percent male. Ninety percent of the females attended college, 78 percent of the males attended college. A management trainee is selected at random. What is the probability that the person selected is a female who did NOT attend college?
A. 0.20
B. 0.08
C. 0.25
D. 0.80

In a management trainee program, 80 percent of the trainees are female, 20 percent male. Ninety percent of the females attended college, 78 percent of the males attended college. A management trainee is selected at random. What is the probability that the person selected is a female who did attend college?
A. 0.20
B. 0.08
C. 0.25
D. 0.72

In a management trainee program, 80 percent of the trainees are female, 20 percent male. Ninety percent of the females attended college, 78 percent of the males attended college. A management trainee is selected at random. What is the probability that the person selected is a male who did NOT attend college?
A. 0.044
B. 0.440
C. 0.256
D. 0.801

In a management trainee program, 80 percent of the trainees are female, 20 percent male. Ninety percent of the females attended college, 78 percent of the males attended college. A management trainee is selected at random. What is the probability that the person selected is a male who did NOT attend college?
A. P (male) P (did not attend college | male)
B. P (did not attend college) P (male | did not attend college)
C. P (male) P (did not attend college)
D. P (did not attend college)

In a management trainee program, 80 percent of the trainees are female, 20 percent male. Ninety percent of the females attended college, 78 percent of the males attended college. A management trainee is selected at random. What is the probability that the person selected is a female who did attend college?
A. P (female) P(did not attend college | female)
B. P (did attend college) P (female | did not attend college)
C. P (female) P(did attend college | female)
D. P (did attend college)

Three defective electric toothbrushes were accidentally shipped to a drugstore by the manufacturer along with 17 non-defective ones. What is the probability that the first two electric toothbrushes sold will be returned to the drugstore because they are defective?
A. 3/20 or 0.15
B. 3/17 or 0.176
C. ¼ or 0.25
D. 3/190 or 0.01579

An electronics firm sells four models of stereo receivers, three CD decks, and six speaker brands. When the four types of components are sold together, they form a “system.” How many different systems can the electronics firm offer?
A. 36
B. 18
C. 72
D. 144

The numbers 0 through 9 are used in code groups of four to identify an item of clothing. Code 1083 might identify a blue blouse, size medium. The code group 2031 might identify a pair of pants, size 18, and so on. Repetitions of numbers are not permitted, i.e., the same number cannot be used more than once in a total sequence. As examples, 2256, 2562 or 5559 would not be permitted. How many different code groups can be designed?
A. 5,040
B. 620
C. 10,200
D. 120

How many permutations of the two letters C and D are possible?
A. 1
B. 0
C. 2
D. 8

You have the assignment of designing color codes for different parts. Three colors are used on each part, but a combination of three colors used for one part cannot be rearranged and used to identify a different part. This means that if green, yellow and violet were used to identify a camshaft, yellow, violet and green (or any other combination of these three colors) could not be used to identify a pinion gear. If there are 35 combinations, how many colors were available?
A. 5
B. 7
C. 9
D. 11

A builder has agreed NOT to build all “look alike” homes in a new subdivision. The builder has three different interior plans that can be combined with any of the five different home exteriors. How many different homes can be built?
A. 8
B. 10
C. 15
D. 30

Six basic colors are used in decorating a new condominium. They are applied to a unit in groups of four colors. One unit might have gold as the principal color, blue as a complementary color, red as the accent color and touches of white. Another unit might have blue as the principal color, white as the complimentary color, gold as the accent color and touches of red. If repetitions are permitted, how many different units can be decorated?
A. 7,825
B. 25
C. 125
D. 1,296

The ABCD football association is considering a Super Ten Football Conference. The top 10 football teams in the country, based on past records, would be members of the Super Ten Conference. Each team would play every other team in the conference during the season and the team winning the most games would be declared the national champion. How many games would the conference commissioner have to schedule each year? (Remember, Oklahoma versus Michigan is the same as Michigan versus Oklahoma.)
A. 45
B. 50
C. 125
D. 14

A rug manufacturer has decided to use 7 compatible colors in her rugs. However, in weaving a rug, only 5 spindles can be used. In advertising, the rug manufacturer wants to indicate the number of different color groupings for sale. How many color groupings using the seven colors taken five at a time are there? (This assumes that 5 different colors will go into each rug, i.e., there are no repetitions of color.)
A. 120
B. 2,520
C. 6,740
D. 36

The first card selected from a standard 52-card deck was a king. If it is returned to the deck, what is the probability that a king will be drawn on the second selection?
A. 1/4 or 0.25
B. 1/13 or 0.077
C. 12/13 or 0.923
D. 1/3 or 0.33

The first card selected from a standard 52-card deck was a king. If it is NOT returned to the deck, what is the probability that a king will be drawn on the second selection?
A. 1/3 or 0.33
B. 1/51 or 0.0196
C. 3/51 or 0.0588
D. 1/13 or 0.077

Which approach to probability assumes that the events are equally likely?
A. Classical
B. Empirical
C. Subjective
D. Mutually exclusive

An experiment may have:
A. Only one outcome
B. Only two outcomes
C. Two or more outcomes
D. Several events

When are two events mutually exclusive?
A. They overlap on a Venn diagram
B. If one event occurs, then the other cannot
C. Probability of one affects the probability of the other
D. Both a and b

Probabilities are important information when
A. using inferential statistics.
B. applying descriptive statistics.
C. predicting a future outcome.
D. A and C

The result of a particular experiment is called a(n)
A. observation.
B. conditional probability.
C. event.
D. outcome.

The probability of two or more events occurring concurrently is called a(n)
A. conditional probability.
B. empirical probability.
C. joint probability.
D. tree diagram.

The probability of an event that is affected by two or more different events is called a(n)
A. conditional probability.
B. empirical probability.
C. joint probability.
D. tree diagram.

A graphical method used to calculate joint and conditional probabilities is
A. a tree diagram.
B. a Venn diagram.
C. a histogram.
D. inferential statistics.

When an experiment is conducted “without replacement,”
A. events are dependent
B. events are equally likely
C. the experiment can be illustrated with a Venn Diagram
D. the probability of two or more events is computed as a joint probability

If two events are independent, then their joint probability is computed with
A. the special rule of addition
B. the special rule of multiplication
C. the general rule of multiplication
D. Bayes’ theorem

When applying the special rule of addition for mutually exclusive events, the joint probability is:
A. 1
B. .5
C. 0
D. unknown

In a finance class, the final grade is based on three tests. Historically, the instructor tells the class that the joint probability of scoring “A”‘s on the first two tests is 0.5. A student assigns a probability of 0.9 that she will get an “A” on the first test. What is the probability that the student will score an “A” on the second test given that she scored an “A” on the first test?
A. 0.50
B. 0.95
C. 0.55
D. 0.90

When an event’s probability depends on the likelihood of another event, the probability is a(n)
A. conditional probability.
B. empirical probability.
C. joint probability.
D. mutually exclusive probability.

A group of employees of Unique Services will be surveyed about a new pension plan. In-depth interviews with each employee selected in the sample will be conducted. The employees are classified as follows.
What is the probability that the first person selected is classified as a maintenance employee?
A. 0.20
B. 0.50
C. 0.025
D. 1.00

A group of employees of Unique Services will be surveyed about a new pension plan. In-depth interviews with each employee selected in the sample will be conducted. The employees are classified as follows.
What is the probability that the first person selected is either in maintenance or in secretarial?
A. 0.200
B. 0.015
C. 0.059
D. 0.001

A group of employees of Unique Services will be surveyed about a new pension plan. In-depth interviews with each employee selected in the sample will be conducted. The employees are classified as follows.
What is the probability that the first person selected is either in management or in supervision?
A. 0.00
B. 0.06
C. 0.15
D. 0.21

A group of employees of Unique Services will be surveyed about a new pension plan. In-depth interviews with each employee selected in the sample will be conducted. The employees are classified as follows.
What is the probability that the first person selected is a supervisor and in management?
A. 0.00
B. 0.06
C. 0.15
D. 0.21

Each salesperson in a large department store chain is rated on their sales ability and their potential for advancement. The data for the 500 sampled salespeople are summarized in the following table.
What is the probability that a salesperson selected at random has above average sales ability and is an excellent potential for advancement?
A. 0.20
B. 0.50
C. 0.27
D. 0.75

Each salesperson in a large department store chain is rated on their sales ability and their potential for advancement. The data for the 500 sampled salespeople are summarized in the following table.
What is the probability that a salesperson selected at random will have average sales ability and good potential for advancement?
A. 0.09
B. 0.12
C. 0.30
D. 0.525

Each salesperson in a large department store chain is rated on their sales ability and their potential for advancement. The data for the 500 sampled salespeople are summarized in the following table.
What is the probability that a salesperson selected at random will have below average sales ability and fair potential for advancement?
A. 0.032
B. 0.10
C. 0.16
D. 0.32

Each salesperson in a large department store chain is rated on their sales ability and their potential for advancement. The data for the 500 sampled salespeople are summarized in the following table.
What is the probability that a salesperson selected at random will have an excellent potential for advancement given they also have above average sales ability?
A. 0.27
B. 0.60
C. 0.404
D. 0.45

Each salesperson in a large department store chain is rated on their sales ability and their potential for advancement. The data for the 500 sampled salespeople are summarized in the following table.
What is the probability that a salesperson selected at random will have an excellent potential for advancement given they also have average sales ability?
A. 0.27
B. 0.30
C. 0.404
D. 0.45

A study of interior designers’ opinions with respect to the most desirable primary color for executive offices showed that:
What is the probability that a designer does not prefer red?
A. 1.00
B. 0.77
C. 0.73
D. 0.23

A study of interior designers’ opinions with respect to the most desirable primary color for executive offices showed that:
What is the probability that a designer does not prefer yellow?
A. 0.000
B. 0.765
C. 0.885
D. 1.000

A study of interior designers’ opinions with respect to the most desirable primary color for executive offices showed that:
What is the probability that a designer does not prefer blue?
A. 1.0000
B. 0.9075
C. 0.8850
D. 0.7725

An automatic machine inserts mixed vegetables into a plastic bag. Past experience revealed that some packages were underweight and some were overweight, but most of them had satisfactory weight.
What is the probability of selecting three packages that are overweight?
A. 0.0000156
B. 0.0004218
C. 0.0000001
D. 0.075

An automatic machine inserts mixed vegetables into a plastic bag. Past experience revealed that some packages were underweight and some were overweight, but most of them had satisfactory weight.
What is the probability of selecting three packages that are satisfactory?
A. 0.900
B. 0.810
C. 0.729
D. 0.075

Using the terminology of Bayes’ Theorem, a posterior probability can also be defined as:
A. a conditional probability
B. a joint probability
C. 1
D. 0

The process used to calculate the probability of an event given additional information has been obtained through
A. Bayes’ theorem.
B. classical probability.
C. permutation.
D. subjective probability

Fill in the Blank Questions

Complete the following analogy: an experiment relates to outcome, as the role of a die relates to _____.
________________________________________

If a set of events are collectively exhaustive and mutually exclusive, what does the sum of the probabilities equal? ___
________________________________________

When the special rule of multiplication is used, the events must be _______________.
________________________________________

When the special rule of addition is used, the events must be _______________.
________________________________________

The probability of selecting a professor who is male and has a master’s degree is called _______________.
________________________________________

To summarize the frequencies of two nominal or ordinal variables and compute conditional probabilities, what table can be used? _______________
________________________________________

What theorem applies additional information to revise probabilities? _______________
________________________________________

The joint probability of two dependent events, P (A and B), is computed as _______________.
________________________________________

What is the probability that a flipped coin will show heads on four consecutive flips? _______________
________________________________________

What type of diagram is useful when applying Bayes’ Theorem? _______________
________________________________________

In a probability problem with joint probabilities, the sum of all the joint probabilities must equal _______________.
________________________________________

Suppose four heads appeared face up on four tosses of a coin. What is the probability that a head will appear face up in the next toss of the coin? _____
________________________________________

What approach to probability is based on a person’s belief, opinion or judgment? _______
________________________________________

If there are five vacant parking places and five automobiles arrive at the same time, in how many different ways they can park? _____
________________________________________

A collection of one or more possible outcomes of an experiment is called an ___________.
________________________________________

A new computer game has been developed and 80 veteran game players will test its market potential. If sixty players liked the game, what is the probability that any veteran game player will like the new computer game? _______
________________________________________

One card will be randomly selected from a standard 52-card deck of cards. What is the probability that it will be the jack of hearts? _____
________________________________________

The number of times an event occurred in the past is divided by the total number of occurrences. What is this approach to probability called? ____________________
________________________________________

What is the probability that a one-spot, two-spot, or six-spot will appear face up on the throw of one die? ______
________________________________________

What is a measured or observed activity called? _________________
________________________________________

What is a particular result of an experiment called? __________
________________________________________

What is a collection of one or more basic outcomes called? __________
________________________________________

To apply the special rule of addition, what must be true about the events? __________
________________________________________

What are two events called when the occurrence of one event does not affect the occurrence of the other event? __________________
________________________________________

What is it called when the order of a set of objects selected from a single group is important? _________
________________________________________

Short Answer Questions

A cell phone salesperson has kept records on the customers who visited the store. 40% of the customers who visited the store were female. Furthermore, the data show that 35% of the females who visited his store purchased a cell phone, while 20% of the males who visited his store purchased a cell phone. Let represent the event that a customer is a female, represent the event that a customer is a male, and B represent the event that a customer will purchase a phone.
What is the probability that a female customer will purchase a cell phone? ______________

A cell phone salesperson has kept records on the customers who visited the store. 40% of the customers who visited the store were female. Furthermore, the data show that 35% of the females who visited his store purchased a cell phone, while 20% of the males who visited his store purchased a cell phone. Let represent the event that a customer is a female, represent the event that a customer is a male, and B represent the event that a customer will purchase a phone.
What is the probability that a male customer will purchase a cell phone? ______________

A company set up a kiosk in the Mall of America for several hours and asked randomly selected people which color cell phone was their favorite. The results follow:
What is the probability that a person would select orange as their favorite color?

A company set up a kiosk in the Mall of America for several hours and asked randomly selected people which color cell phone was their favorite. The results follow:
What is the probability that a person would select orange or lime as their favorite color?

A company set up a kiosk in the Mall of America for several hours and asked randomly selected people which color cell phone was their favorite. The results follow:
What is an outcome of this experiment?

A company’s managers evaluated their employees into three classes: excellent performance, good performance, and poor performance. The following is a frequency distribution of the results.
What is the probability that a randomly selected employee was rated excellent or good?

In flipping a fair coin, what is the probability of either a head or a tail on one toss?

In flipping a fair coin, what is the probability of a head and a tail on one toss?

In flipping a fair coin, what is the probability of a head and a tail on two tosses?

Airlines monitor the causes of flights arriving late. 75% of flights are late because of weather, 35% of flights are late because of ground operations. 10% of flights are late because of weather and ground operations. What is the joint probability that a flight arrives late because of weather and ground operations?

Airlines monitor the causes of flights arriving late. 75% of flights are late because of weather, 35% of flights are late because of ground operations. 15% of flights are late because of weather and ground operations. What is the probability that a flight arrives late because of weather or ground operations?

In a survey of employee satisfaction, 60% of the employees are male and 45% of the employees are satisfied. What is the probability of randomly selecting an employee who is male and satisfied?

In a card deck of 52 cards, what is the probability of selecting two kings from the deck without replacement?

In a survey of employee satisfaction, the following table summarizes the results in terms of employee satisfaction and gender.
What is the probability that an employee is Female and Dissatisfied?

In a survey of employee satisfaction, the following table summarizes the results in terms of employee satisfaction and gender.
What is the probability that an employee is Male or Dissatisfied?

In a survey of employee satisfaction, the following table summarizes the results in terms of employee satisfaction and gender.
What is the probability that an employee is Satisfied given that the employee is Male?

A company set up a kiosk in the Mall of America for several hours and asked randomly selected people which color cell phone cover was their favorite. The results follow:
What is the probability of randomly selecting a person who likes white cell phones the best?

A company set up a kiosk in the Mall of America for several hours and asked randomly selected people which color cell phone cover was their favorite. The results follow:
What is the probability that black or orange are the favorite colors?

A company set up a kiosk in the Mall of America for several hours and asked randomly selected people which color cell phone cover was their favorite. The results follow:
What is the probability that orange is the favorite color given that the person’s age is less than 21?

A company set up a kiosk in the Mall of America for several hours and asked randomly selected people which color cell phone cover was their favorite. The results follow:
What is the probability that black is the favorite color given that the person’s age is 21 or older?

A company set up a kiosk in the Mall of America for several hours and asked randomly selected people which color cell phone cover was their favorite. The results follow:
What is the probability that black is the favorite color given that the person’s age is 21 or older?

A company set up a kiosk in the Mall of America for several hours and asked randomly selected people which color cell phone cover was their favorite. The results follow:
What is the probability that black, lime or orange are the favorite colors given that the person’s age is 21 or older?

Dice are used in a variety of games. A die is a six sided cube with a number of dots on each side. The number of dots ranges from one to six. If two die are used on a game, how many outcomes are possible?

In a study of student preference of energy drinks, the researcher has identified a population of 10 students. To get a quick result, the researcher will select a sample of 2 students. How many different samples are possible?

A student organization of 10 wants to select a president, a vice-president, and treasurer. How many different leadership assignments are possible?

Essay Questions

Draw a Venn diagram showing the probability for two mutually exclusive events and a Venn diagram showing the probability for two events that are not mutually exclusive. Explain the difference in the two diagrams.

Compare and contrast the classical, empirical, and subjective approaches to assigning probabilities.

What is the difference between a permutation and a combination?

When are two outcomes independent? Explain in terms of the rules of probability.

Chapter 05 A Survey of Probability Concepts Answer Key

True / False Questions

The probability of rolling a 3 or 2 on a single die is an example of conditional probability.
FALSE

AACSB: Communication Abilities
Bloom’s: Comprehension
Difficulty: Medium
Learning Objective: 05-06 Define the term conditional probability.
Topic: Rules of Multiplication

The probability of rolling a 3 or 2 on a single die is an example of mutually exclusive events.
TRUE

AACSB: Communication Abilities
Bloom’s: Comprehension
Difficulty: Medium
Learning Objective: 05-02 Identify and apply the appropriate approach to assigning probabilities.
Topic: Approaches to assigning probabilities

An individual can assign a subjective probability to an event based on the individual’s knowledge about the event.
TRUE

AACSB: Communication Abilities
Bloom’s: Knowledge
Difficulty: Medium
Learning Objective: 05-02 Identify and apply the appropriate approach to assigning probabilities.
Topic: Approaches to assigning probabilities

To apply the special rule of addition, the events must be mutually exclusive.
TRUE

AACSB: Communication Abilities
Bloom’s: Comprehension
Difficulty: Medium
Learning Objective: 05-03 Calculate probabilities using the rules of addition.
Topic: Rules of Addition

A joint probability measures the likelihood that two or more events will happen concurrently.
TRUE

AACSB: Communication Abilities
Bloom’s: Knowledge
Difficulty: Medium
Learning Objective: 05-04 Define the term joint probability.
Topic: Rules of Addition

The joint probability of two independent events, A and B, is computed as: P(A and B) = P(A) P(B).
TRUE

AACSB: Communication Abilities
Bloom’s: Knowledge
Difficulty: Medium
Learning Objective: 05-05 Calculate probabilities using the rules of multiplication.
Topic: Rules of Multiplication

The joint probability of two events, A and B, that are not independent is computed as: P(A and B) = P(A) P(B|A).
TRUE

AACSB: Communication Abilities
Bloom’s: Knowledge
Difficulty: Medium
Learning Objective: 05-06 Define the term conditional probability.
Topic: Rules of Multiplication

A coin is tossed four times. The joint probability that all four tosses will result in a head is ¼ or 0.25.
FALSE

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-05 Calculate probabilities using the rules of multiplication.
Topic: Rules of Multiplication

If there are ‘m’ ways of doing one thing and ‘n’ ways of doing another thing, the multiplication formula states that there are (m) · (n) ways of doing both.
TRUE

AACSB: Communication Abilities
Bloom’s: Knowledge
Difficulty: Medium
Learning Objective: 05-09 Determine the number of outcomes using the appropriate principle of counting.
Topic: Principles of Counting

A combination of a set of objects is defined by the order of the objects.
FALSE

The complement rule states that the probability of an event not occurring is equal to one minus the probability of its occurrence.
TRUE

If two events are mutually exclusive, then P(A or B) = P(A) P(B).
FALSE

AACSB: Communication Abilities
Bloom’s: Comprehension
Difficulty: Medium
Learning Objective: 05-04 Define the term joint probability.
Topic: Rules of Addition

An illustration of an experiment is turning the ignition key of an automobile as it comes off the assembly line to determine whether or not the engine will start.
TRUE

AACSB: Communication Abilities
Bloom’s: Comprehension
Difficulty: Medium
Learning Objective: 05-01 Explain the terms experiment; event; and outcome.
Topic: What is probability?

Bayes’ theorem is a method to revise the probability of an event given additional information.
TRUE

AACSB: Communication Abilities
Bloom’s: Knowledge
Difficulty: Medium
Learning Objective: 05-08 Calculate probabilities using Bayes’ theorem.
Topic: Bayes’ Theorem

Bayes’ theorem is used to calculate a subjective probability.
FALSE

AACSB: Communication Abilities
Bloom’s: Comprehension
Difficulty: Medium
Learning Objective: 05-08 Calculate probabilities using Bayes’ theorem.
Topic: Bayes’ Theorem

Multiple Choice Questions

The National Center for Health Statistics reported that of every 883 deaths in recent years, 24 resulted from an automobile accident, 182 from cancer and 333 from heart disease. What is the probability that a particular death is due to an automobile accident?
A.24/883 or 0.027
B. 539/883 or 0.610
C. 24/333 or 0.072
D. 182/883 or 0.206

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-02 Identify and apply the appropriate approach to assigning probabilities.
Topic: Approaches to assigning probabilities

If two events A and B are mutually exclusive, what does the special rule of addition state?
A.P(A or B) = P(A) + P(B)
B. P(A and B) = P(A) + P(B)
C. P(A and/or B) = P(A) + P(B)
D. P(A or B) = P(A) – P(B)

AACSB: Communication Abilities
Bloom’s: Comprehension
Difficulty: Medium
Learning Objective: 05-03 Calculate probabilities using the rules of addition.
Topic: Rules of Addition

What does the complement rule state?
A.P(A) = P(A) – P(B)
B. P(A) = 1 – P(not A)
C. P(A) = P(A) · P(B)
D. P(A) = P(A)X + P(B)

AACSB: Communication Abilities
Bloom’s: Knowledge
Difficulty: Medium
Learning Objective: 05-03 Calculate probabilities using the rules of addition.
Topic: Rules of Addition

Which approach to probability is exemplified by the following formula?
Probability of an Event =

A. Classical approach
B. Empirical approach
C. Subjective approach
D. None of the above

A study of 200 computer service firms revealed these incomes after taxes:
What is the probability that a particular firm selected has $1 million or more in income after taxes?
A. 0.00
B. 0.25
C. 0.49
D. 0.51

A firm offers routine physical examinations as part of a health service program for its employees. The exams showed that 8% of the employees needed corrective shoes, 15% needed major dental work and 3% needed both corrective shoes and major dental work. What is the probability that an employee selected at random will need either corrective shoes or major dental work?
A.0.20
B. 0.25
C. 0.50
D. 1.00

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-04 Define the term joint probability.
Topic: Rules of Addition

A survey of top executives revealed that 35% of them regularly read Time magazine, 20% read Newsweek and 40% read U.S. News & World Report. Ten percent read both Time and U.S. News & World Report. What is the probability that a particular top executive reads either Time or U.S. News & World Report regularly?
A.0.85
B. 0.06
C. 1.00
D. 0.65

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-04 Define the term joint probability.
Topic: Rules of Addition

A study by the National Park Service revealed that 50% of the vacationers going to the Rocky Mountain region visit Yellowstone Park, 40% visit the Grand Tetons and 35% visit both. What is the probability that a vacationer will visit at least one of these magnificent attractions?
A.0.95
B. 0.35
C. 0.55
D. 0.05

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-04 Define the term joint probability.
Topic: Rules of Addition

A tire manufacturer advertises, “the median life of our new all-season radial tire is 50,000 miles. An immediate adjustment will be made on any tire that does not last 50,000 miles.” You purchased four of these tires. What is the probability that all four tires will wear out before traveling 50,000 miles?
A.1/10 or 0.10
B. ¼ or 0.25
C. 1/64 or 0.0156
D. 1/16 or 0.0625

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-05 Calculate probabilities using the rules of multiplication.
Topic: Rules of Multiplication

A sales representative calls on four hospitals in Westchester County. It is immaterial what order he calls on them. How many ways can he organize his calls?
A.4
B. 24
C. 120
D. 37

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-09 Determine the number of outcomes using the appropriate principle of counting.
Topic: Principles of Counting

There are 10 rolls of film in a box and 3 are defective. Two rolls are selected without replacement. What is the probability of selecting a defective roll followed by another defective roll?
A.½ or 0.50
B. ¼ or 0.25
C. 1/120 or about 0.0083
D. 1/15 or about 0.07

AACSB: Reflective Thinking
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-06 Define the term conditional probability.
Topic: Rules of Multiplication

Giorgio offers the person who purchases an 8 ounce bottle of Allure two free gifts, either an umbrella, a 1 ounce bottle of Midnight, a feminine shaving kit, a raincoat or a pair of rain boots. If you purchased Allure what is the probability you randomly selected an umbrella and a shaving kit in that order?
A.0.00
B. 1.00
C. 0.05
D. 0.20

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-06 Define the term conditional probability.
Topic: Rules of Multiplication

A board of directors consists of eight men and four women. A four-member search committee is randomly chosen to recommend a new company president. What is the probability that all four members of the search committee will be women?
A.1/120 or 0.00083
B. 1/16 or 0.0625
C. ⅛ or 0.125
D. 1/495 or 0.002

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-06 Define the term conditional probability.
Topic: Rules of Multiplication

A lamp manufacturer has developed five lamp bases and four lampshades that could be used together. How many different arrangements of base and shade can be offered?
A.5
B. 10
C. 15
D. 20

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-09 Determine the number of outcomes using the appropriate principle of counting.
Topic: Principles of Counting

A gumball machine has just been filled with 50 black, 150 white, 100 red and 100 yellow gum balls that have been thoroughly mixed. Sue and Jim, each, purchased one gumball. What is the likelihood both Sue and Jim get red gumballs?
A.0.50
B. 0.062
C. 0.33
D. 0.75

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-06 Define the term conditional probability.
Topic: Rules of Multiplication

What does equal?
A.640
B. 36
C. 10
D. 120

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-09 Determine the number of outcomes using the appropriate principle of counting.
Topic: Principles of Counting

In a management trainee program, 80 percent of the trainees are female, 20 percent male. Ninety percent of the females attended college, 78 percent of the males attended college. A management trainee is selected at random. What is the probability that the person selected is a female who did NOT attend college?
A.0.20
B. 0.08
C. 0.25
D. 0.80

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-06 Define the term conditional probability.
Topic: Rules of Multiplication

In a management trainee program, 80 percent of the trainees are female, 20 percent male. Ninety percent of the females attended college, 78 percent of the males attended college. A management trainee is selected at random. What is the probability that the person selected is a female who did attend college?
A.0.20
B. 0.08
C. 0.25
D. 0.72

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-06 Define the term conditional probability.
Topic: Rules of Multiplication

In a management trainee program, 80 percent of the trainees are female, 20 percent male. Ninety percent of the females attended college, 78 percent of the males attended college. A management trainee is selected at random. What is the probability that the person selected is a male who did NOT attend college?
A.0.044
B. 0.440
C. 0.256
D. 0.801

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-06 Define the term conditional probability.
Topic: Rules of Multiplication

In a management trainee program, 80 percent of the trainees are female, 20 percent male. Ninety percent of the females attended college, 78 percent of the males attended college. A management trainee is selected at random. What is the probability that the person selected is a male who did NOT attend college?
A.P (male) P (did not attend college | male)
B. P (did not attend college) P (male | did not attend college)
C. P (male) P (did not attend college)
D. P (did not attend college)

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-06 Define the term conditional probability.
Topic: Rules of Multiplication

In a management trainee program, 80 percent of the trainees are female, 20 percent male. Ninety percent of the females attended college, 78 percent of the males attended college. A management trainee is selected at random. What is the probability that the person selected is a female who did attend college?
A.P (female) P(did not attend college | female)
B. P (did attend college) P (female | did not attend college)
C. P (female) P(did attend college | female)
D. P (did attend college)

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-06 Define the term conditional probability.
Topic: Rules of Multiplication

Three defective electric toothbrushes were accidentally shipped to a drugstore by the manufacturer along with 17 non-defective ones. What is the probability that the first two electric toothbrushes sold will be returned to the drugstore because they are defective?
A.3/20 or 0.15
B. 3/17 or 0.176
C. ¼ or 0.25
D. 3/190 or 0.01579

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-06 Define the term conditional probability.
Topic: Rules of Multiplication

An electronics firm sells four models of stereo receivers, three CD decks, and six speaker brands. When the four types of components are sold together, they form a “system.” How many different systems can the electronics firm offer?
A.36
B. 18
C. 72
D. 144

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-09 Determine the number of outcomes using the appropriate principle of counting.
Topic: Principles of Counting

The numbers 0 through 9 are used in code groups of four to identify an item of clothing. Code 1083 might identify a blue blouse, size medium. The code group 2031 might identify a pair of pants, size 18, and so on. Repetitions of numbers are not permitted, i.e., the same number cannot be used more than once in a total sequence. As examples, 2256, 2562 or 5559 would not be permitted. How many different code groups can be designed?
A.5,040
B. 620
C. 10,200
D. 120

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-09 Determine the number of outcomes using the appropriate principle of counting.
Topic: Principles of Counting

How many permutations of the two letters C and D are possible?
A.1
B. 0
C. 2
D. 8

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-09 Determine the number of outcomes using the appropriate principle of counting.
Topic: Principles of Counting

You have the assignment of designing color codes for different parts. Three colors are used on each part, but a combination of three colors used for one part cannot be rearranged and used to identify a different part. This means that if green, yellow and violet were used to identify a camshaft, yellow, violet and green (or any other combination of these three colors) could not be used to identify a pinion gear. If there are 35 combinations, how many colors were available?
A.5
B. 7
C. 9
D. 11

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Hard
Learning Objective: 05-09 Determine the number of outcomes using the appropriate principle of counting.
Topic: Principles of Counting

A builder has agreed NOT to build all “look alike” homes in a new subdivision. The builder has three different interior plans that can be combined with any of the five different home exteriors. How many different homes can be built?
A.8
B. 10
C. 15
D. 30

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-09 Determine the number of outcomes using the appropriate principle of counting.
Topic: Principles of Counting

Six basic colors are used in decorating a new condominium. They are applied to a unit in groups of four colors. One unit might have gold as the principal color, blue as a complementary color, red as the accent color and touches of white. Another unit might have blue as the principal color, white as the complimentary color, gold as the accent color and touches of red. If repetitions are permitted, how many different units can be decorated?
A.7,825
B. 25
C. 125
D. 1,296

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Hard
Learning Objective: 05-09 Determine the number of outcomes using the appropriate principle of counting.
Topic: Principles of Counting

The ABCD football association is considering a Super Ten Football Conference. The top 10 football teams in the country, based on past records, would be members of the Super Ten Conference. Each team would play every other team in the conference during the season and the team winning the most games would be declared the national champion. How many games would the conference commissioner have to schedule each year? (Remember, Oklahoma versus Michigan is the same as Michigan versus Oklahoma.)
A.45
B. 50
C. 125
D. 14

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-09 Determine the number of outcomes using the appropriate principle of counting.
Topic: Principles of Counting

A rug manufacturer has decided to use 7 compatible colors in her rugs. However, in weaving a rug, only 5 spindles can be used. In advertising, the rug manufacturer wants to indicate the number of different color groupings for sale. How many color groupings using the seven colors taken five at a time are there? (This assumes that 5 different colors will go into each rug, i.e., there are no repetitions of color.)
A.120
B. 2,520
C. 6,740
D. 36

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Hard
Learning Objective: 05-09 Determine the number of outcomes using the appropriate principle of counting.
Topic: Principles of Counting

The first card selected from a standard 52-card deck was a king. If it is returned to the deck, what is the probability that a king will be drawn on the second selection?
A.1/4 or 0.25
B. 1/13 or 0.077
C. 12/13 or 0.923
D. 1/3 or 0.33

The first card selected from a standard 52-card deck was a king. If it is NOT returned to the deck, what is the probability that a king will be drawn on the second selection?
A.1/3 or 0.33
B. 1/51 or 0.0196
C. 3/51 or 0.0588
D. 1/13 or 0.077

Which approach to probability assumes that the events are equally likely?
A.Classical
B. Empirical
C. Subjective
D. Mutually exclusive

An experiment may have:
A.Only one outcome
B. Only two outcomes
C. Two or more outcomes
D. Several events

AACSB: Communication Abilities
Bloom’s: Comprehension
Difficulty: Medium
Learning Objective: 05-01 Explain the terms experiment; event; and outcome.
Topic: What is probability?

When are two events mutually exclusive?
A.They overlap on a Venn diagram
B. If one event occurs, then the other cannot
C. Probability of one affects the probability of the other
D. Both a and b

Probabilities are important information when
A.using inferential statistics.
B. applying descriptive statistics.
C. predicting a future outcome.
D. A and C

AACSB: Communication Abilities
Bloom’s: Comprehension
Difficulty: Medium
Learning Objective: 05-01 Explain the terms experiment; event; and outcome.
Topic: What is probability?

The result of a particular experiment is called a(n)
A.observation.
B. conditional probability.
C. event.
D. outcome.

AACSB: Communication Abilities
Bloom’s: Knowledge
Difficulty: Easy
Learning Objective: 05-01 Explain the terms experiment; event; and outcome.
Topic: What is probability?

The probability of two or more events occurring concurrently is called a(n)
A.conditional probability.
B. empirical probability.
C. joint probability.
D. tree diagram.

AACSB: Communication Abilities
Bloom’s: Knowledge
Difficulty: Easy
Learning Objective: 05-05 Calculate probabilities using the rules of multiplication.
Topic: Rules of Multiplication

The probability of an event that is affected by two or more different events is called a(n)
A.conditional probability.
B. empirical probability.
C. joint probability.
D. tree diagram.

AACSB: Communication Abilities
Bloom’s: Knowledge
Difficulty: Easy
Learning Objective: 05-06 Define the term conditional probability.
Topic: Rules of Multiplication

A graphical method used to calculate joint and conditional probabilities is
A.a tree diagram.
B. a Venn diagram.
C. a histogram.
D. inferential statistics.

AACSB: Communication Abilities
Bloom’s: Knowledge
Difficulty: Easy
Learning Objective: 05-05 Calculate probabilities using the rules of multiplication.
Topic: Rules of Multiplication

When an experiment is conducted “without replacement,”
A.events are dependent
B. events are equally likely
C. the experiment can be illustrated with a Venn Diagram
D. the probability of two or more events is computed as a joint probability

AACSB: Communication Abilities
Bloom’s: Comprehension
Difficulty: Easy
Learning Objective: 05-06 Define the term conditional probability.
Topic: Rules of Multiplication

If two events are independent, then their joint probability is computed with
A.the special rule of addition
B. the special rule of multiplication
C. the general rule of multiplication
D. Bayes’ theorem

AACSB: Communication Abilities
Bloom’s: Comprehension
Difficulty: Easy
Learning Objective: 05-05 Calculate probabilities using the rules of multiplication.
Topic: Rules of Multiplication

When applying the special rule of addition for mutually exclusive events, the joint probability is:
A.1
B. .5
C. 0
D. unknown

AACSB: Communication Abilities
Bloom’s: Comprehension
Difficulty: Easy
Learning Objective: 05-05 Calculate probabilities using the rules of multiplication.
Topic: Rules of Multiplication

In a finance class, the final grade is based on three tests. Historically, the instructor tells the class that the joint probability of scoring “A”‘s on the first two tests is 0.5. A student assigns a probability of 0.9 that she will get an “A” on the first test. What is the probability that the student will score an “A” on the second test given that she scored an “A” on the first test?
A.0.50
B. 0.95
C. 0.55
D. 0.90

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Hard
Learning Objective: 05-08 Calculate probabilities using Bayes’ theorem.
Topic: Bayes’ Theorem

When an event’s probability depends on the likelihood of another event, the probability is a(n)
A.conditional probability.
B. empirical probability.
C. joint probability.
D. mutually exclusive probability.

AACSB: Communication Abilities
Bloom’s: Comprehension
Difficulty: Easy
Learning Objective: 05-06 Define the term conditional probability.
Topic: Rules of Multiplication

A group of employees of Unique Services will be surveyed about a new pension plan. In-depth interviews with each employee selected in the sample will be conducted. The employees are classified as follows.
What is the probability that the first person selected is classified as a maintenance employee?
A. 0.20
B. 0.50
C. 0.025
D. 1.00

A group of employees of Unique Services will be surveyed about a new pension plan. In-depth interviews with each employee selected in the sample will be conducted. The employees are classified as follows.
What is the probability that the first person selected is either in maintenance or in secretarial?
A. 0.200
B. 0.015
C. 0.059
D. 0.001

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-03 Calculate probabilities using the rules of addition.
Topic: Rules of Addition

A group of employees of Unique Services will be surveyed about a new pension plan. In-depth interviews with each employee selected in the sample will be conducted. The employees are classified as follows.
What is the probability that the first person selected is either in management or in supervision?
A. 0.00
B. 0.06
C. 0.15
D. 0.21

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-03 Calculate probabilities using the rules of addition.
Topic: Rules of Addition

A group of employees of Unique Services will be surveyed about a new pension plan. In-depth interviews with each employee selected in the sample will be conducted. The employees are classified as follows.
What is the probability that the first person selected is a supervisor and in management?
A. 0.00
B. 0.06
C. 0.15
D. 0.21

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-03 Calculate probabilities using the rules of addition.
Topic: Rules of Addition

Each salesperson in a large department store chain is rated on their sales ability and their potential for advancement. The data for the 500 sampled salespeople are summarized in the following table.
What is the probability that a salesperson selected at random has above average sales ability and is an excellent potential for advancement?
A.0.20
B. 0.50
C. 0.27
D. 0.75

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-07 Compute probabilities using a contingency table.
Topic: Contingency Tables

Each salesperson in a large department store chain is rated on their sales ability and their potential for advancement. The data for the 500 sampled salespeople are summarized in the following table.
What is the probability that a salesperson selected at random will have average sales ability and good potential for advancement?
A. 0.09
B. 0.12
C. 0.30
D. 0.525

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-07 Compute probabilities using a contingency table.
Topic: Contingency Tables

Each salesperson in a large department store chain is rated on their sales ability and their potential for advancement. The data for the 500 sampled salespeople are summarized in the following table.
What is the probability that a salesperson selected at random will have below average sales ability and fair potential for advancement?
A. 0.032
B. 0.10
C. 0.16
D. 0.32

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-07 Compute probabilities using a contingency table.
Topic: Contingency Tables

Each salesperson in a large department store chain is rated on their sales ability and their potential for advancement. The data for the 500 sampled salespeople are summarized in the following table.
What is the probability that a salesperson selected at random will have an excellent potential for advancement given they also have above average sales ability?
A. 0.27
B. 0.60
C. 0.404
D. 0.45

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-07 Compute probabilities using a contingency table.
Topic: Contingency Tables

Each salesperson in a large department store chain is rated on their sales ability and their potential for advancement. The data for the 500 sampled salespeople are summarized in the following table.
What is the probability that a salesperson selected at random will have an excellent potential for advancement given they also have average sales ability?
A. 0.27
B. 0.30
C. 0.404
D. 0.45

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-07 Compute probabilities using a contingency table.
Topic: Contingency Tables

A study of interior designers’ opinions with respect to the most desirable primary color for executive offices showed that:
What is the probability that a designer does not prefer red?
A. 1.00
B. 0.77
C. 0.73
D. 0.23

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-04 Define the term joint probability.
Topic: Rules of Addition

A study of interior designers’ opinions with respect to the most desirable primary color for executive offices showed that:
What is the probability that a designer does not prefer yellow?
A. 0.000
B. 0.765
C. 0.885
D. 1.000

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-04 Define the term joint probability.
Topic: Rules of Addition

A study of interior designers’ opinions with respect to the most desirable primary color for executive offices showed that:
What is the probability that a designer does not prefer blue?
A. 1.0000
B. 0.9075
C. 0.8850
D. 0.7725

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-04 Define the term joint probability.
Topic: Rules of Addition

An automatic machine inserts mixed vegetables into a plastic bag. Past experience revealed that some packages were underweight and some were overweight, but most of them had satisfactory weight.
What is the probability of selecting three packages that are overweight?
A. 0.0000156
B. 0.0004218
C. 0.0000001
D. 0.075

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-05 Calculate probabilities using the rules of multiplication.
Topic: Rules of Multiplication

An automatic machine inserts mixed vegetables into a plastic bag. Past experience revealed that some packages were underweight and some were overweight, but most of them had satisfactory weight.
What is the probability of selecting three packages that are satisfactory?
A. 0.900
B. 0.810
C. 0.729
D. 0.075

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-05 Calculate probabilities using the rules of multiplication.
Topic: Rules of Multiplication

Using the terminology of Bayes’ Theorem, a posterior probability can also be defined as:
A.a conditional probability
B. a joint probability
C. 1
D. 0

AACSB: Communication Abilities
Bloom’s: Comprehension
Difficulty: Easy
Learning Objective: 05-08 Calculate probabilities using Bayes’ theorem.
Topic: Bayes’ Theorem

The process used to calculate the probability of an event given additional information has been obtained through
A.Bayes’ theorem.
B. classical probability.
C. permutation.
D. subjective probability

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Hard
Learning Objective: 05-08 Calculate probabilities using Bayes’ theorem.
Topic: Bayes’ Theorem

Fill in the Blank Questions

Complete the following analogy: an experiment relates to outcome, as the role of a die relates to _____.
any one value between 1 and 6

AACSB: Communication Abilities
Bloom’s: Comprehension
Difficulty: Medium
Learning Objective: 05-01 Explain the terms experiment; event; and outcome.
Topic: What is probability?

If a set of events are collectively exhaustive and mutually exclusive, what does the sum of the probabilities equal? ___
1

When the special rule of multiplication is used, the events must be _______________.
independent

AACSB: Communication Abilities
Bloom’s: Comprehension
Difficulty: Medium
Learning Objective: 05-05 Calculate probabilities using the rules of multiplication.
Topic: Rules of Multiplication

When the special rule of addition is used, the events must be _______________.
mutually exclusive

AACSB: Communication Abilities
Bloom’s: Comprehension
Difficulty: Medium
Learning Objective: 05-03 Calculate probabilities using the rules of addition.
Topic: Rules of Addition

The probability of selecting a professor who is male and has a master’s degree is called _______________.
Joint probability

AACSB: Communication Abilities
Bloom’s: Comprehension
Difficulty: Medium
Learning Objective: 05-04 Define the term joint probability.
Topic: Rules of Addition

To summarize the frequencies of two nominal or ordinal variables and compute conditional probabilities, what table can be used? _______________
Contingency table

AACSB: Communication Abilities
Bloom’s: Comprehension
Difficulty: Medium
Learning Objective: 05-07 Compute probabilities using a contingency table.
Topic: Contingency Tables

What theorem applies additional information to revise probabilities? _______________
Bayes’ Theorem

AACSB: Communication Abilities
Bloom’s: Comprehension
Difficulty: Medium
Learning Objective: 05-08 Calculate probabilities using Bayes’ theorem.
Topic: Bayes’ Theorem

The joint probability of two dependent events, P (A and B), is computed as _______________.
P(A and B) = P(A) P(B|A)

AACSB: Communication Abilities
Bloom’s: Comprehension
Difficulty: Medium
Learning Objective: 05-06 Define the term conditional probability.
Topic: Rules of Multiplication

What is the probability that a flipped coin will show heads on four consecutive flips? _______________
0.0625

AACSB: Analytic Skills
Bloom’s: Comprehension
Difficulty: Medium
Learning Objective: 05-05 Calculate probabilities using the rules of multiplication.
Topic: Rules of Multiplication

What type of diagram is useful when applying Bayes’ Theorem? _______________
A tree diagram

AACSB: Communication Abilities
Bloom’s: Comprehension
Difficulty: Medium
Learning Objective: 05-08 Calculate probabilities using Bayes’ theorem.
Topic: Bayes’ Theorem

In a probability problem with joint probabilities, the sum of all the joint probabilities must equal _______________.
1 or one

AACSB: Reflective Thinking
Bloom’s: Comprehension
Difficulty: Hard
Learning Objective: 05-04 Define the term joint probability.
Topic: Rules of Addition

Suppose four heads appeared face up on four tosses of a coin. What is the probability that a head will appear face up in the next toss of the coin? _____
1/2 or 0.5

What approach to probability is based on a person’s belief, opinion or judgment? _______
Subjective

If there are five vacant parking places and five automobiles arrive at the same time, in how many different ways they can park? _____
120

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-09 Determine the number of outcomes using the appropriate principle of counting.
Topic: Principles of Counting

A collection of one or more possible outcomes of an experiment is called an ___________.
event

AACSB: Communication Abilities
Bloom’s: Knowledge
Difficulty: Medium
Learning Objective: 05-01 Explain the terms experiment; event; and outcome.
Topic: What is probability?

A new computer game has been developed and 80 veteran game players will test its market potential. If sixty players liked the game, what is the probability that any veteran game player will like the new computer game? _______
3/4 or 0.75

One card will be randomly selected from a standard 52-card deck of cards. What is the probability that it will be the jack of hearts? _____
1/52 or 0.0192

The number of times an event occurred in the past is divided by the total number of occurrences. What is this approach to probability called? ____________________
Empirical

What is the probability that a one-spot, two-spot, or six-spot will appear face up on the throw of one die? ______
1/2 or 0.5

What is a measured or observed activity called? _________________
Experiment

AACSB: Communication Abilities
Bloom’s: Knowledge
Difficulty: Medium
Learning Objective: 05-01 Explain the terms experiment; event; and outcome.
Topic: What is probability?

What is a particular result of an experiment called? __________
Outcome

AACSB: Communication Abilities
Bloom’s: Knowledge
Difficulty: Medium
Learning Objective: 05-01 Explain the terms experiment; event; and outcome.
Topic: What is probability?

What is a collection of one or more basic outcomes called? __________
Event

AACSB: Communication Abilities
Bloom’s: Knowledge
Difficulty: Medium
Learning Objective: 05-01 Explain the terms experiment; event; and outcome.
Topic: What is probability?

To apply the special rule of addition, what must be true about the events? __________
Mutually exclusive

AACSB: Communication Abilities
Bloom’s: Comprehension
Difficulty: Medium
Learning Objective: 05-03 Calculate probabilities using the rules of addition.
Topic: Rules of Addition

What are two events called when the occurrence of one event does not affect the occurrence of the other event? __________________
Independent

AACSB: Communication Abilities
Bloom’s: Knowledge
Difficulty: Medium
Learning Objective: 05-06 Define the term conditional probability.
Topic: Rules of Multiplication

What is it called when the order of a set of objects selected from a single group is important? _________
Permutation

Short Answer Questions

A cell phone salesperson has kept records on the customers who visited the store. 40% of the customers who visited the store were female. Furthermore, the data show that 35% of the females who visited his store purchased a cell phone, while 20% of the males who visited his store purchased a cell phone. Let represent the event that a customer is a female, represent the event that a customer is a male, and B represent the event that a customer will purchase a phone.
What is the probability that a female customer will purchase a cell phone? ______________

P(B|A1) = .35

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-08 Calculate probabilities using Bayes’ theorem.
Topic: Bayes’ Theorem

A cell phone salesperson has kept records on the customers who visited the store. 40% of the customers who visited the store were female. Furthermore, the data show that 35% of the females who visited his store purchased a cell phone, while 20% of the males who visited his store purchased a cell phone. Let represent the event that a customer is a female, represent the event that a customer is a male, and B represent the event that a customer will purchase a phone.
What is the probability that a male customer will purchase a cell phone? ______________

P(B|A2) = .20

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-08 Calculate probabilities using Bayes’ theorem.
Topic: Bayes’ Theorem

A company set up a kiosk in the Mall of America for several hours and asked randomly selected people which color cell phone was their favorite. The results follow:
What is the probability that a person would select orange as their favorite color?

0.35 or 35%

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Easy
Learning Objective: 05-02 Identify and apply the appropriate approach to assigning probabilities.
Topic: Approaches to assigning probabilities

A company set up a kiosk in the Mall of America for several hours and asked randomly selected people which color cell phone was their favorite. The results follow:
What is the probability that a person would select orange or lime as their favorite color?

0.60 or 60%

A company set up a kiosk in the Mall of America for several hours and asked randomly selected people which color cell phone was their favorite. The results follow:
What is an outcome of this experiment?

Any one of the colors is a correct answer

AACSB: Reflective Thinking
Bloom’s: Knowledge
Difficulty: Easy
Learning Objective: 05-01 Explain the terms experiment; event; and outcome.
Topic: What is probability?

A company’s managers evaluated their employees into three classes: excellent performance, good performance, and poor performance. The following is a frequency distribution of the results.
What is the probability that a randomly selected employee was rated excellent or good?

0.95 or 95%

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Easy
Learning Objective: 05-03 Calculate probabilities using the rules of addition.
Topic: Rules of Addition

In flipping a fair coin, what is the probability of either a head or a tail on one toss?

1.0 or 100%

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Easy
Learning Objective: 05-03 Calculate probabilities using the rules of addition.
Topic: Rules of Addition

In flipping a fair coin, what is the probability of a head and a tail on one toss?

0.00 or 0%

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Easy
Learning Objective: 05-03 Calculate probabilities using the rules of addition.
Topic: Rules of Addition

In flipping a fair coin, what is the probability of a head and a tail on two tosses?

0.50 or 50%

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Easy
Learning Objective: 05-05 Calculate probabilities using the rules of multiplication.
Topic: Rules of Multiplication

Airlines monitor the causes of flights arriving late. 75% of flights are late because of weather, 35% of flights are late because of ground operations. 10% of flights are late because of weather and ground operations. What is the joint probability that a flight arrives late because of weather and ground operations?

10% or 0.10

AACSB: Reflective Thinking
Bloom’s: Comprehension
Difficulty: Easy
Learning Objective: 05-04 Define the term joint probability.
Topic: Rules of Addition

Airlines monitor the causes of flights arriving late. 75% of flights are late because of weather, 35% of flights are late because of ground operations. 15% of flights are late because of weather and ground operations. What is the probability that a flight arrives late because of weather or ground operations?

95% or 0.95

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Easy
Learning Objective: 05-04 Define the term joint probability.
Topic: Rules of Addition

In a survey of employee satisfaction, 60% of the employees are male and 45% of the employees are satisfied. What is the probability of randomly selecting an employee who is male and satisfied?

0.27

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-05 Calculate probabilities using the rules of multiplication.
Topic: Rules of Multiplication

In a card deck of 52 cards, what is the probability of selecting two kings from the deck without replacement?

0.0045

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-06 Define the term conditional probability.
Topic: Rules of Multiplication

In a survey of employee satisfaction, the following table summarizes the results in terms of employee satisfaction and gender.
What is the probability that an employee is Female and Dissatisfied?

0.22

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Hard
Learning Objective: 05-07 Compute probabilities using a contingency table.
Topic: Contingency Tables

In a survey of employee satisfaction, the following table summarizes the results in terms of employee satisfaction and gender.
What is the probability that an employee is Male or Dissatisfied?

0.82

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Hard
Learning Objective: 05-07 Compute probabilities using a contingency table.
Topic: Contingency Tables

In a survey of employee satisfaction, the following table summarizes the results in terms of employee satisfaction and gender.
What is the probability that an employee is Satisfied given that the employee is Male?

0.45

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Hard
Learning Objective: 05-07 Compute probabilities using a contingency table.
Topic: Contingency Tables

A company set up a kiosk in the Mall of America for several hours and asked randomly selected people which color cell phone cover was their favorite. The results follow:
What is the probability of randomly selecting a person who likes white cell phones the best?

0.075

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-03 Calculate probabilities using the rules of addition.
Topic: Rules of Addition

A company set up a kiosk in the Mall of America for several hours and asked randomly selected people which color cell phone cover was their favorite. The results follow:
What is the probability that black or orange are the favorite colors?

0.65

A company set up a kiosk in the Mall of America for several hours and asked randomly selected people which color cell phone cover was their favorite. The results follow:
What is the probability that orange is the favorite color given that the person’s age is less than 21?

0.35

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-06 Define the term conditional probability.
Topic: Rules of Multiplication

A company set up a kiosk in the Mall of America for several hours and asked randomly selected people which color cell phone cover was their favorite. The results follow:
What is the probability that black is the favorite color given that the person’s age is 21 or older?

0.50

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-06 Define the term conditional probability.
Topic: Rules of Multiplication

A company set up a kiosk in the Mall of America for several hours and asked randomly selected people which color cell phone cover was their favorite. The results follow:
What is the probability that black is the favorite color given that the person’s age is 21 or older?

0.50

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-06 Define the term conditional probability.
Topic: Rules of Multiplication

A company set up a kiosk in the Mall of America for several hours and asked randomly selected people which color cell phone cover was their favorite. The results follow:
What is the probability that black, lime or orange are the favorite colors given that the person’s age is 21 or older?

0.90

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-07 Compute probabilities using a contingency table.
Topic: Contingency Tables

Dice are used in a variety of games. A die is a six sided cube with a number of dots on each side. The number of dots ranges from one to six. If two die are used on a game, how many outcomes are possible?

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-09 Determine the number of outcomes using the appropriate principle of counting.
Topic: Principles of Counting

In a study of student preference of energy drinks, the researcher has identified a population of 10 students. To get a quick result, the researcher will select a sample of 2 students. How many different samples are possible?

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-09 Determine the number of outcomes using the appropriate principle of counting.
Topic: Principles of Counting

A student organization of 10 wants to select a president, a vice-president, and treasurer. How many different leadership assignments are possible?

720

AACSB: Analytic Skills
Bloom’s: Application
Difficulty: Medium
Learning Objective: 05-09 Determine the number of outcomes using the appropriate principle of counting.
Topic: Principles of Counting

Essay Questions

Draw a Venn diagram showing the probability for two mutually exclusive events and a Venn diagram showing the probability for two events that are not mutually exclusive. Explain the difference in the two diagrams.

The main difference is that the two areas representing probability do not overlap for mutually exclusive events and the two areas do overlap when the two events are not mutually exclusive. In summary, the joint probability is equal to 0 when the events are mutually exclusive, and the joint probability is greater than 0 but less than 1 when the events are not mutually exclusive.

AACSB: Reflective Thinking
Bloom’s: Application
Difficulty: Hard
Learning Objective: 05-03 Calculate probabilities using the rules of addition.
Learning Objective: 05-04 Define the term joint probability.
Topic: Rules of Addition

Compare and contrast the classical, empirical, and subjective approaches to assigning probabilities.

The classical method requires that all outcomes of an experiment are known and can be listed. Then, the probabilities can be computed. Examples that apply the classical approach to probability include problems involving card decks and dice. The empirical method is applied when all the experimental outcomes cannot be listed so that we need to collect data to compute probabilities. Then probabilities are computed as the frequency of the desired outcome divided by the total number of observations. The subjective approach is applied when data is not readily available and a person assigns their best guess to the probability of an outcome.

AACSB: Reflective Thinking
Bloom’s: Comprehension
Difficulty: Hard
Learning Objective: 05-02 Identify and apply the appropriate approach to assigning probabilities.
Topic: Approaches to assigning probabilities

What is the difference between a permutation and a combination?

Both methods compute the number of possible outcomes for a given problem. When the order of the possible outcomes is important to the problem, we compute the number of permutations. When the order of the possible outcomes is not important, then we compute the number of combinations. For example, if we select outcomes A, B, and C, from the set {A, B, C, D, E, F}, the events {A, B, C} and {C, B, A} would count as one combination. However because the order is different, they count as two permutations. For a given problem there would always be more permutations than combinations.

AACSB: Reflective Thinking
Bloom’s: Comprehension
Difficulty: Hard
Learning Objective: 05-09 Determine the number of outcomes using the appropriate principle of counting.
Topic: Principles of Counting

When are two outcomes independent? Explain in terms of the rules of probability.

Two outcomes are independent when the probability of one outcome is not affected by the probability of the second outcome. In terms of conditional probabilities, two outcomes, A and B are independent when P(A ) = P(A|B). This notation says that the probability of A given B is equal to the probability of A. In other words, the probability of A is unaffected by B.

AACSB: Reflective Thinking
Bloom’s: Comprehension
Difficulty: Hard
Learning Objective: 05-05 Calculate probabilities using the rules of multiplication.
Topic: Rules of Multiplication

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