Statistical Techniques In Business and Economics 16th Edition by Lind - Test Bank Instant Download - Complete Test Bank With Answers Sample Questions Are Posted Below Chapter 05 A Survey of Probability Concepts True / False Questions 1. The probability of rolling a 3 or 2 on a single die …
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Statistical Techniques In Business and Economics 16th Edition by Lind – Test Bank
Instant Download – Complete Test Bank With Answers
Sample Questions Are Posted Below
Chapter 05
A Survey of Probability Concepts
True / False Questions
| 1. | The probability of rolling a 3 or 2 on a single die is an example of conditional probability.
True False |
| 2. | The probability of rolling a 3 or 2 on a single die is an example of mutually exclusive events.
True False |
| 3. | An individual can assign a subjective probability to an event based on the individual’s knowledge about the event.
True False |
| 4. | To apply the special rule of addition, the events must be mutually exclusive.
True False |
| 5. | A joint probability measures the likelihood that two or more events will happen concurrently.
True False |
| 6. | The joint probability of two independent events, A and B, is computed as P(A and B) = P(A) P(B).
True False |
| 7. | 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 |
| 8. | 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 |
| 9. | 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 |
| 10. | A combination of a set of objects is defined by the order of the objects.
True False |
| 11. | The complement rule states that the probability of an event not occurring is equal to one minus the probability of its occurrence.
True False |
| 12. | If two events are mutually exclusive, then P(A and B) = P(A)P(B).
True False |
| 13. | 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 |
| 14. | Bayes’ theorem is a method to revise the probability of an event given additional information.
True False |
| 15. | Bayes’ theorem is used to calculate a subjective probability.
True False |
Multiple Choice Questions
| 16. | 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?
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| 17. | If two events A and B are mutually exclusive, what does the special rule of addition state?
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| 18. | What does the complement rule state?
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| 19. | Which approach to probability is exemplified by the following formula?
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| 20. | 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?
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| 21. | 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?
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| 22. | 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. A total of 10% 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?
|
| 23. | 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?
|
| 24. | 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?
|
| 25. | 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?
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| 26. | There are 10 AAA batteries in a box and 3 are defective. Two batteries are selected without replacement. What is the probability of selecting a defective battery followed by another defective battery?
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| 27. | Giorgio offers the person who purchases an 8-ounce bottle of Allure two free gifts, chosen from the following: 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?
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| 28. | 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?
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| 29. | A lamp manufacturer designed five lamp bases and four lampshades that could be used together. How many different arrangements of base and shade can be offered?
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| 30. | A gumball machine has just been filled with 50 black, 150 white, 100 red, and 100 yellow gumballs that have been thoroughly mixed. Sue and Jim each purchase one gumball. What is the likelihood that both Sue and Jim will get red gumballs?
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| 31. | What does equal?
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| 32. | In a management trainee program, 80% of the trainees are female, while 20% are male. Ninety percent of the females attended college; 78% 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?
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| 33. | In a management trainee program, 80% of the trainees are female, while 20% are male. Ninety percent of the females attended college; 78% of the males attended college. A management trainee is selected at random. What is the probability that the person selected is a female who attended college?
|
| 34. | In a management trainee program, 80% of the trainees are female, while 20% are male. Ninety percent of the females attended college; 78% 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?
|
| 35. | In a management trainee program, 80% of the trainees are female, while 20% are male. Ninety percent of the females attended college; 78% 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?
|
| 36. | In a management trainee program, 80% of the trainees are female, while 20% are male. Ninety percent of the females attended college; 78% of the males attended college. A management trainee is selected at random. What is the probability that the person selected is a female who attended college?
|
| 37. | A supplier delivers an order for 20 electric toothbrushes to a store. By accident, three of the electric toothbrushes are defective. What is the probability that the first two electric toothbrushes sold will be returned because they are defective?
|
| 38. | An electronics firm sells four models of stereo receivers, three amplifiers, 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?
|
| 39. | 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—in other words, the same number cannot be used more than once in a total sequence. As examples, 2,256, 2,562, or 5,559 would not be permitted. How many different code groups can be designed?
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| 40. | How many permutations of the three letters C, D, and E are possible?
|
| 41. | You are assigned to design color codes for different parts. Three colors are used to code on each part. Once a combination of three colors is used—such as green, yellow, and red—these three colors cannot be rearranged to use as a code for another part. If there are 35 combinations, how many colors are available?
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| 42. | A developer of a new subdivision wants to build homes that are all different. There are three different interior plans that can be combined with any of five different home exteriors. How many different homes can be built?
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| 43. | 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 complementary color, gold as the accent color, and touches of red. If repetitions are permitted, how many different units can be decorated?
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| 44. | 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.)
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| 45. | A rug manufacturer has decided to use seven compatible colors in her rugs. However, in weaving a rug, only five 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 five different colors will go into each rug—in other words, there are no repetitions of color.)
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| 46. | 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?
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| 47. | 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?
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| 48. | Which approach to probability assumes that the events are equally likely?
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| 49. | An experiment may have ____________.
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| 50. | When are two experimental outcomes mutually exclusive?
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| 51. | Probabilities are important information when __________.
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| 52. | The result of a particular experiment is called a(n) ___________.
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| 53. | The probability of two or more events occurring concurrently is called a(n) _________.
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| 54. | The probability of an event that is affected by two or more different events is called a(n) ___________.
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| 55. | A graphical method used to calculate joint and conditional probabilities is __________.
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| 56. | When an experiment is conducted “without replacement,” __________.
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| 57. | If two events are independent, then their joint probability is computed with _________.
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| 58. | When applying the special rule of addition for mutually exclusive events, the joint probability is _______.
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| 59. | When an event’s probability depends on the likelihood of another event, the probability is a(n) ___________.
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| 60. | 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?
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| 61. | 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?
|
| 62. | 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?
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| 63. | 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?
|
| 64. | The process used to calculate the probability of an event given additional information has been obtained through:
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| 65. | 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 has excellent potential for advancement?
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| 66. | 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?
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| 67. | 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?
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| 68. | 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?
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| 69. | 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?
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| 70. | A study of interior designers’ opinions with respect to the most desirable primary color for executive offices showed the following:
What is the probability that a designer does not prefer red?
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| 71. | A study of interior designers’ opinions with respect to the most desirable primary color for executive offices showed the following:
What is the probability that a designer does not prefer yellow?
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| 72. | A study of interior designers’ opinions with respect to the most desirable primary color for executive offices showed the following:
What is the probability that a designer does not prefer blue?
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| 73. | 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?
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| 74. | 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?
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| 75. | 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?
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| 76. | Using the terminology of Bayes’ theorem, a posterior probability can also be defined as:
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| 77. | If A and B are mutually exclusive events with P(A) = 0.2 and P(B) = 0.6, then P(A or B) = _____.
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| 78. | If P(A) = 0.62, P(B) = 0.47, and P(A or B) = 0.88, then P(A and B) = _____.
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| 79. | A method of assigning probabilities based upon judgment, opinions, and available information is referred to as the:
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| 80. | Your favorite soccer team has two remaining matches to complete the season. The possible outcomes of a soccer match are win, lose, or tie. What is the possible number of outcomes for the season?
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Fill in the Blank Questions
| 81. | Complete the following analogy: An experiment relates to outcome, as the role of a die relates to _____.
________________________________________ |
| 82. | If a set of outcomes is collectively exhaustive and mutually exclusive, the sum of the probabilities equals __________.
________________________________________ |
| 83. | When the special rule of multiplication is used, the events must be _______________.
________________________________________ |
| 84. | When the special rule of addition is used, the events must be _______________.
________________________________________ |
| 85. | The probability of selecting a professor who is male and has a master’s degree is called a ______________.
________________________________________ |
| 86. | To summarize the frequencies of two nominal or ordinal variables and compute conditional probabilities, a ___________ can be used.
________________________________________ |
| 87. | The joint probability of two events that are not independent, P(A and B), is computed as _______________.
________________________________________ |
| 88. | The probability that a flipped coin will show heads on four consecutive flips is _______________.
________________________________________ |
| 89. | In a tree diagram that illustrates the joint probabilities for a probability problem, the sum of all the joint probabilities must equal _______________.
________________________________________ |
| 90. | Suppose you toss a coin four times and get heads four times (no tails). The probability that heads will appear on the next toss of the coin is ____.
________________________________________ |
| 91. | The _________ approach to probability is based on a person’s belief, opinion, or judgment.
________________________________________ |
| 92. | If there are five vacant parking places and five automobiles arrive at the same time, the number of different ways they can park is ____.
________________________________________ |
| 93. | A collection of one or more possible outcomes of an experiment is called a(n) ___________.
________________________________________ |
| 94. | A new computer game has been developed and 80 veteran game players will test its market potential. If 60 players liked the game, the probability that any veteran game player will like the new computer game is ______.
________________________________________ |
| 95. | One card will be randomly selected from a standard 52-card deck. The probability that it will be the jack of hearts is ____.
________________________________________ |
| 96. | The theorem that applies additional information to revise probabilities is called ________.
________________________________________ |
| 97. | A probability is calculated by dividing the number of desired outcomes by the total number of occurrences. This approach to probability is called __________.
________________________________________ |
| 98. | The probability that a one, two, or six will appear face up on the throw of one die is _____.
________________________________________ |
| 99. | A measured or observed activity is called a(n) ___________.
________________________________________ |
| 100. | The particular result of an experiment is called a(n) _________.
________________________________________ |
| 101. | A collection of one or more basic outcomes is called a(n) _________.
________________________________________ |
| 102. | To apply the special rule of addition, the events must be _________.
________________________________________ |
| 103. | Two events are called _________ when the occurrence of one event does not affect the occurrence of the other event.
________________________________________ |
| 104. | When the order of a set of objects selected from a single group is important, this is called ________.
________________________________________ |
| 105. | A ________ is useful when applying Bayes’ theorem.
________________________________________ |
Essay Questions
| 106. | 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?
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| 107. | 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?
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| 108. | 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?
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| 109. | 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?
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| 110. | In flipping a fair coin, what is the probability of either heads or tails on one toss?
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| 111. | In flipping a fair coin, what is the probability of both heads and tails on one toss?
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| 112. | In flipping a fair coin, what is the probability of heads and tails on two tosses?
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| 113. | Airlines monitor the causes of flights arriving late. A total of 75% of flights are late because of weather, while 35% of flights are late because of ground operations. A full 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?
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| 114. | Airlines monitor the causes of flights arriving late. A total of 75% of flights are late because of weather, while 35% of flights are late because of ground operations. A full 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?
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| 115. | 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?
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| 116. | In a deck of 52 cards, what is the probability of selecting two kings from the deck without replacement?
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| 117. | 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?
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| 118. | 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?
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| 119. | 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?
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| 120. | 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?
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| 121. | 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?
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| 122. | 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?
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| 123. | 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?
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| 124. | 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 red is the favorite color, given that the person’s age is 21 or older?
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| 125. | 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?
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| 126. | 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 in a game, how many outcomes are possible?
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| 127. | 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 two students. How many different samples are possible?
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| 128. | A student organization of 10 wants to select a president, a vice-president, and a treasurer. How many different leadership assignments are possible?
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| 129. | Draw a Venn diagram showing the probability for two mutually exclusive events and also draw a Venn diagram showing the probability for two events that are not mutually exclusive. Explain the difference in the two diagrams.
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| 130. | Compare and contrast the classical, empirical, and subjective approaches to assigning probabilities.
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| 131. | What is the difference between a permutation and a combination?
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| 132. | When are two outcomes independent? Explain in terms of the rules of probability.
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| 133. | A cell phone salesperson has kept records on the customers who visited his store. Forty percent 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 A1 represent the event that a customer is a female, A2 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?
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| 134. | A cell phone salesperson has kept records on the customers who visited his store. Forty percent 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 A1 represent the event that a customer is a female, A2 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?
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Chapter 05 A Survey of Probability Concepts Answer Key
True / False Questions
| 1. | The probability of rolling a 3 or 2 on a single die is an example of conditional probability.
FALSE This is classical probability. |
| AACSB: Communication Accessibility: Keyboard Navigation Blooms: Understand Difficulty: 2 Medium Learning Objective: 05-04 Calculate probabilities using the rules of multiplication. Topic: Rules of Multiplication to Calculate Probabilities |
| 2. | The probability of rolling a 3 or 2 on a single die is an example of mutually exclusive events.
TRUE |
| AACSB: Communication Accessibility: Keyboard Navigation Blooms: Understand Difficulty: 2 Medium Learning Objective: 05-02 Assign probabilities using a classical; empirical; or subjective approach. Topic: Approaches to Assigning Probabilities |
| 3. | An individual can assign a subjective probability to an event based on the individual’s knowledge about the event.
TRUE |
| AACSB: Communication Accessibility: Keyboard Navigation Blooms: Remember Difficulty: 2 Medium Learning Objective: 05-02 Assign probabilities using a classical; empirical; or subjective approach. Topic: Approaches to Assigning Probabilities |
| 4. | To apply the special rule of addition, the events must be mutually exclusive.
TRUE |
| AACSB: Communication Accessibility: Keyboard Navigation Blooms: Understand Difficulty: 2 Medium Learning Objective: 05-03 Calculate probabilities using the rules of addition. Topic: Rules of Addition for Computing Probabilities |
| 5. | A joint probability measures the likelihood that two or more events will happen concurrently.
TRUE |
| AACSB: Communication Accessibility: Keyboard Navigation Blooms: Remember Difficulty: 2 Medium Learning Objective: 05-03 Calculate probabilities using the rules of addition. Topic: Rules of Addition for Computing Probabilities |
| 6. | The joint probability of two independent events, A and B, is computed as P(A and B) = P(A) P(B).
TRUE |
| AACSB: Communication Accessibility: Keyboard Navigation Blooms: Remember Difficulty: 2 Medium Learning Objective: 05-04 Calculate probabilities using the rules of multiplication. Topic: Rules of Multiplication to Calculate Probabilities |
| 7. | 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 Accessibility: Keyboard Navigation Blooms: Remember Difficulty: 2 Medium Learning Objective: 05-04 Calculate probabilities using the rules of multiplication. Topic: Rules of Multiplication to Calculate Probabilities |
| 8. | A coin is tossed four times. The joint probability that all four tosses will result in a head is ¼ or 0.25.
FALSE Each outcome’s probability is .5. The joint probability is (.5)(.5)(.5)(.5) = 0.0625. |
| AACSB: Analytic Accessibility: Keyboard Navigation Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-04 Calculate probabilities using the rules of multiplication. Topic: Rules of Multiplication to Calculate Probabilities |
| 9. | 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 Accessibility: Keyboard Navigation Blooms: Remember Difficulty: 2 Medium Learning Objective: 05-07 Determine the number of outcomes using principles of counting. Topic: Principles of Counting |
| 10. | A combination of a set of objects is defined by the order of the objects.
FALSE The order of objects is important for permutations. |
| AACSB: Communication Accessibility: Keyboard Navigation Blooms: Remember Difficulty: 2 Medium Learning Objective: 05-07 Determine the number of outcomes using principles of counting. Topic: Principles of Counting |
| 11. | The complement rule states that the probability of an event not occurring is equal to one minus the probability of its occurrence.
TRUE |
| AACSB: Communication Accessibility: Keyboard Navigation Blooms: Remember Difficulty: 2 Medium Learning Objective: 05-02 Assign probabilities using a classical; empirical; or subjective approach. Topic: Approaches to Assigning Probabilities |
| 12. | If two events are mutually exclusive, then P(A and B) = P(A)P(B).
FALSE If two events are mutually exclusive, then P(A and B) = P(A) + P(B). |
| AACSB: Communication Accessibility: Keyboard Navigation Blooms: Understand Difficulty: 2 Medium Learning Objective: 05-03 Calculate probabilities using the rules of addition. Topic: Rules of Addition for Computing Probabilities |
| 13. | 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 Accessibility: Keyboard Navigation Blooms: Understand Difficulty: 2 Medium Learning Objective: 05-01 Define the terms probability; experiment; event; and outcome. Topic: What is a Probability? |
| 14. | Bayes’ theorem is a method to revise the probability of an event given additional information.
TRUE |
| AACSB: Communication Accessibility: Keyboard Navigation Blooms: Remember Difficulty: 1 Easy Learning Objective: 05-06 Calculate probabilities using Bayes’ theorem. Topic: Bayes’ Theorem |
| 15. | Bayes’ theorem is used to calculate a subjective probability.
FALSE |
| AACSB: Communication Accessibility: Keyboard Navigation Blooms: Remember Difficulty: 1 Easy Learning Objective: 05-06 Calculate probabilities using Bayes’ theorem. Topic: Bayes’ Theorem |
Multiple Choice Questions
| 16. | 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?
Based on the empirical approach to probability, 24/883 = 0.027. |
| AACSB: Analytic Accessibility: Keyboard Navigation Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-02 Assign probabilities using a classical; empirical; or subjective approach. Topic: Approaches to Assigning Probabilities |
| 17. | If two events A and B are mutually exclusive, what does the special rule of addition state?
By definition. P(A or B) = P(A) + P(B) is the special rule of addition. |
| AACSB: Communication Accessibility: Keyboard Navigation Blooms: Remember Difficulty: 2 Medium Learning Objective: 05-03 Calculate probabilities using the rules of addition. Topic: Rules of Addition for Computing Probabilities |
| 18. | What does the complement rule state?
By definition, P(A) plus its complement, P(not A) must equal 1. |
| AACSB: Communication Accessibility: Keyboard Navigation Blooms: Remember Difficulty: 2 Medium Learning Objective: 05-03 Calculate probabilities using the rules of addition. Topic: Rules of Addition for Computing Probabilities |
| 19. | Which approach to probability is exemplified by the following formula?
The Empirical Rule is based on the frequency of observed experimental outcomes. |
| AACSB: Communication Blooms: Remember Difficulty: 2 Medium Learning Objective: 05-02 Assign probabilities using a classical; empirical; or subjective approach. Topic: Approaches to Assigning Probabilities |
| 20. | 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 couple of approaches can be used to answer the question. Using the complement rule, the probability of firms less than $1 million is 102/200 = 0.51. The complement or firms with $1 million or more income is 1.0 – 0.51 = 0.49. |
| AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-02 Assign probabilities using a classical; empirical; or subjective approach. Topic: Approaches to Assigning Probabilities |
| 21. | 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?
The two events, corrective shoes and dental work, are not mutually exclusive because an employee can need both. The P(corrective shoes or dental work) = P(corrective shoes) + P(dental work) – P(corrective shoes and dental work) = 0.8 + 0.15 – 0.03 = 0.20. |
| AACSB: Analytic Accessibility: Keyboard Navigation Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-03 Calculate probabilities using the rules of addition. Topic: Rules of Addition for Computing Probabilities |
| 22. | 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. A total of 10% 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?
The three events—reading Time, Newsweek, or U.S. News—are not mutually exclusive because executives can read more than one of the magazines. The P(Time or U.S. News) = P(Time) + P(U.S. News) – P(Time and U.S. News) = 0.35 + 0.40 – 0.10 = 0.65. |
| AACSB: Analytic Accessibility: Keyboard Navigation Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-03 Calculate probabilities using the rules of addition. Topic: Rules of Addition for Computing Probabilities |
| 23. | 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?
The two events, visiting Yellowstone and visiting the Grand Tetons, are not mutually exclusive because vacationers can visit both locations. The P(Yellowstone or Grand Tetons) = P(Yellowstone) + P(Grand Tetons) – P(Yellowstone and Grand Tetons) = 0.50 + 0.40 – 0.35 = 0.55. |
| AACSB: Analytic Accessibility: Keyboard Navigation Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-03 Calculate probabilities using the rules of addition. Topic: Rules of Addition for Computing Probabilities |
| 24. | 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?
The median corresponds with the 50th percentile. So the probability that a tire wears out before 50,000 miles is 0.5. Each outcome’s probability is .5. The joint probability is (.5)(.5)(.5)(.5) = 0.0625. |
| AACSB: Analytic Accessibility: Keyboard Navigation Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-04 Calculate probabilities using the rules of multiplication. Topic: Rules of Multiplication to Calculate Probabilities |
| 25. | 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?
Use the multiplication formula: (4)(3)(2)(1) = 24. |
| AACSB: Analytic Accessibility: Keyboard Navigation Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-07 Determine the number of outcomes using principles of counting. Topic: Principles of Counting |
| 26. | There are 10 AAA batteries in a box and 3 are defective. Two batteries are selected without replacement. What is the probability of selecting a defective battery followed by another defective battery?
The probability of a defective battery on the first selection is 3/10 = .3. The probability of selecting a second defective battery is a conditional probability that assumes the first selection was defective, so the probability of a second defective battery is 2/9. The joint probability is (3/10)(2/9) = 0.066667. |
| AACSB: Reflective Thinking Accessibility: Keyboard Navigation Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-04 Calculate probabilities using the rules of multiplication. Topic: Rules of Multiplication to Calculate Probabilities |
| 27. | Giorgio offers the person who purchases an 8-ounce bottle of Allure two free gifts, chosen from the following: 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?
There are five different gifts. Therefore, the probability of any gift is 1/5 = .2. The probability of selecting a second gift is a conditional probability that assumes the first selection was an umbrella, so the probability of a second gift, a shaving kit, is ¼ = 0.25. The joint probability is (1/5)(1/4) = 1/20 = 0.05. |
| AACSB: Analytic Accessibility: Keyboard Navigation Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-04 Calculate probabilities using the rules of multiplication. Topic: Rules of Multiplication to Calculate Probabilities |
| 28. | 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?
There are four women in a group of 12 individuals. Therefore, the probability of picking a woman on the first selection is 4/12, the second selection is 3/11, the third selection is 2/10, and the fourth is 1/9. This is an application of the multiplication rule for events that are not independent. The joint probability is (4/12)(3/11)(2/10)(1/9) = 0.002. |
| AACSB: Analytic Accessibility: Keyboard Navigation Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-04 Calculate probabilities using the rules of multiplication. Topic: Rules of Multiplication to Calculate Probabilities |
| 29. | A lamp manufacturer designed five lamp bases and four lampshades that could be used together. How many different arrangements of base and shade can be offered?
Using the multiplication formula, (5)(4) = 20. |
| AACSB: Analytic Accessibility: Keyboard Navigation Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-07 Determine the number of outcomes using principles of counting. Topic: Principles of Counting |
| 30. | A gumball machine has just been filled with 50 black, 150 white, 100 red, and 100 yellow gumballs that have been thoroughly mixed. Sue and Jim each purchase one gumball. What is the likelihood that both Sue and Jim will get red gumballs?
The probability of a red gumball on the first selection is 100/400 = .25. The probability of selecting a second red gumball is a conditional probability that assumes the first selection was a red gumball, so the probability of a second red gumball is 99/399. The Joint probability is (100/400)(99/399) = 0.062. |
| AACSB: Analytic Accessibility: Keyboard Navigation Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-04 Calculate probabilities using the rules of multiplication. Topic: Rules of Multiplication to Calculate Probabilities |
| 31. | What does equal?
(6*5*4*3*2*1)(2*1)/(4*3*2*1)(3*2*1) = 10 |
| AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-07 Determine the number of outcomes using principles of counting. Topic: Principles of Counting |
| 32. | In a management trainee program, 80% of the trainees are female, while 20% are male. Ninety percent of the females attended college; 78% 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?
First, the conditional probability that a person attended college given the person is female is P(college | female) = 0.9. The complement is P(no college | female) = 0.1. Now the joint probability of selecting a female who did not attend college is P(female and no college) = P(female) P(no college | female) = (0.8)(0.1) = 0.08. |
| AACSB: Analytic Accessibility: Keyboard Navigation Blooms: Apply Difficulty: 3 Hard Learning Objective: 05-04 Calculate probabilities using the rules of multiplication. Topic: Rules of Multiplication to Calculate Probabilities |
| 33. | In a management trainee program, 80% of the trainees are female, while 20% are male. Ninety percent of the females attended college; 78% of the males attended college. A management trainee is selected at random. What is the probability that the person selected is a female who attended college?
First, the conditional probability that a person attended college given the person is female is P(college | female) = 0.9. Now the joint probability of selecting a female who did attend college is P(female and college) = P(female) P(college | female) = (0.8)(0.9) = 0.72. |
| AACSB: Analytic Accessibility: Keyboard Navigation Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-04 Calculate probabilities using the rules of multiplication. Topic: Rules of Multiplication to Calculate Probabilities |
| 34. | In a management trainee program, 80% of the trainees are female, while 20% are male. Ninety percent of the females attended college; 78% 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?
First, the conditional probability that a person attended college given the person is male is P(college | male) = 0.78. The complement is P(no college | male) = 0.22. Now the joint probability of selecting a male who did not attend college is P(male and no college) = P(male) P(no college |male) = (0.2)(0.22) = 0.044. |
| AACSB: Analytic Accessibility: Keyboard Navigation Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-04 Calculate probabilities using the rules of multiplication. Topic: Rules of Multiplication to Calculate Probabilities |
| 35. | In a management trainee program, 80% of the trainees are female, while 20% are male. Ninety percent of the females attended college; 78% 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?
First, the conditional probability that a person attended college given the person is male. The complement is P(no college | male). Now the joint probability of selecting a male who did not attend college is P(male and no college) = P(male) P(no college | male). |
| AACSB: Analytic Accessibility: Keyboard Navigation Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-04 Calculate probabilities using the rules of multiplication. Topic: Rules of Multiplication to Calculate Probabilities |
| 36. | In a management trainee program, 80% of the trainees are female, while 20% are male. Ninety percent of the females attended college; 78% of the males attended college. A management trainee is selected at random. What is the probability that the person selected is a female who attended college?
First, the conditional probability that a person attended college given the person is female. The complement is P(no college | female). Now the joint probability of selecting a female who did not attend college is P(female and no college) = P(female) P(no college | female). |
| AACSB: Analytic Accessibility: Keyboard Navigation Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-04 Calculate probabilities using the rules of multiplication. Topic: Rules of Multiplication to Calculate Probabilities |
| 37. | A supplier delivers an order for 20 electric toothbrushes to a store. By accident, three of the electric toothbrushes are defective. What is the probability that the first two electric toothbrushes sold will be returned because they are defective?
The probability of a defective unit on the first selection is 3/20 = 0.15. The probability of selecting a second unit is a conditional probability that assumes the first selection was defective, so the probability of a second defective toothbrush is 2/19. The joint probability is (3/20)(2/19) = 0.01579. |
| AACSB: Analytic Accessibility: Keyboard Navigation Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-04 Calculate probabilities using the rules of multiplication. Topic: Rules of Multiplication to Calculate Probabilities |
| 38. | An electronics firm sells four models of stereo receivers, three amplifiers, 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?
Using the multiplication formula, (4)(3)(6) = 72. |
| AACSB: Analytic Accessibility: Keyboard Navigation Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-07 Determine the number of outcomes using principles of counting. Topic: Principles of Counting |
| 39. | 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—in other words, the same number cannot be used more than once in a total sequence. As examples, 2,256, 2,562, or 5,559 would not be permitted. How many different code groups can be designed?
Using the multiplication formula, (10)(9)(8)(7) = 5040 different codes without repeated digits. |
| AACSB: Analytic Accessibility: Keyboard Navigation Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-07 Determine the number of outcomes using principles of counting. Topic: Principles of Counting |
| 40. | How many permutations of the three letters C, D, and E are possible?
Using the permutation formula 3!/0! = (3)(2)(1) = 6. |
| AACSB: Analytic Accessibility: Keyboard Navigation Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-07 Determine the number of outcomes using principles of counting. Topic: Principles of Counting |
| 41. | You are assigned to design color codes for different parts. Three colors are used to code on each part. Once a combination of three colors is used—such as green, yellow, and red—these three colors cannot be rearranged to use as a code for another part. If there are 35 combinations, how many colors are available?
Using the combination formula, x!/(3!(x – 3)!) or trial and error, there are 7 colors. |
| AACSB: Analytic Accessibility: Keyboard Navigation Blooms: Apply Difficulty: 3 Hard Learning Objective: 05-07 Determine the number of outcomes using principles of counting. Topic: Principles of Counting |
| 42. | A developer of a new subdivision wants to build homes that are all different. There are three different interior plans that can be combined with any of five different home exteriors. How many different homes can be built?
Using the multiplication formula, (3)(5) = 15. |
| AACSB: Analytic Accessibility: Keyboard Navigation Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-07 Determine the number of outcomes using principles of counting. Topic: Principles of Counting |
| 43. | 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 complementary color, gold as the accent color, and touches of red. If repetitions are permitted, how many different units can be decorated?
Using the multiplication formula, (6)(6)(6)(6) = 1,296. |
| AACSB: Analytic Accessibility: Keyboard Navigation Blooms: Apply Difficulty: 3 Hard Learning Objective: 05-07 Determine the number of outcomes using principles of counting. Topic: Principles of Counting |
| 44. | 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.)
Using the combination formula, n = 10 and r = 2, 10!/2!(10 – 2)! = 90/2 = 45. |
| AACSB: Analytic Accessibility: Keyboard Navigation Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-07 Determine the number of outcomes using principles of counting. Topic: Principles of Counting |
| 45. | A rug manufacturer has decided to use seven compatible colors in her rugs. However, in weaving a rug, only five 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 five different colors will go into each rug—in other words, there are no repetitions of color.)
Using the combination formula, n = 7 and r = 5; 7!/5!(7 – 5)! = 42/2 = 21. |
| AACSB: Analytic Accessibility: Keyboard Navigation Blooms: Apply Difficulty: 3 Hard Learning Objective: 05-07 Determine the number of outcomes using principles of counting. Topic: Principles of Counting |
| 46. | 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?
The probability is 4/52 = 1/13, or 0.077. |
| AACSB: Analytic Accessibility: Keyboard Navigation Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-02 Assign probabilities using a classical; empirical; or subjective approach. Topic: Approaches to Assigning Probabilities |
| 47. | 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?
The probability of a king on the first selection is 4/52 = 1/13. The probability of selecting a second king is a conditional probability that assumes the first selection was a king, so the probability of a second king is 3/51, or 0.0588. |
| AACSB: Analytic Accessibility: Keyboard Navigation Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-02 Assign probabilities using a classical; empirical; or subjective approach. Topic: Approaches to Assigning Probabilities |
| 48. | Which approach to probability assumes that the events are equally likely?
By definition, the classical approach assumes that events are equally likely. |
| AACSB: Communication Accessibility: Keyboard Navigation Blooms: Remember Difficulty: 1 Easy Learning Objective: 05-02 Assign probabilities using a classical; empirical; or subjective approach. Topic: Approaches to Assigning Probabilities |
| 49. | An experiment may have ____________.
By definition, an experiment results in one or more outcomes. |
| AACSB: Communication Accessibility: Keyboard Navigation Blooms: Remember Difficulty: 1 Easy Learning Objective: 05-01 Define the terms probability; experiment; event; and outcome. Topic: What is a Probability? |
| 50. | When are two experimental outcomes mutually exclusive?
By example, an experiment measures the variable gender. Therefore, there are two possible outcomes: male or female. The outcome is mutually exclusive since a person can be classified as either male or female, not both. |
| AACSB: Communication Accessibility: Keyboard Navigation Blooms: Understand Difficulty: 2 Medium Learning Objective: 05-02 Assign probabilities using a classical; empirical; or subjective approach. Topic: Approaches to Assigning Probabilities |
| 51. | Probabilities are important information when __________.
Inferential statistics uses sample data to make decisions with a stated probability of making an error. |
| AACSB: Communication Accessibility: Keyboard Navigation Blooms: Understand Difficulty: 2 Medium Learning Objective: 05-01 Define the terms probability; experiment; event; and outcome. Topic: What is a Probability? |
| 52. | The result of a particular experiment is called a(n) ___________.
By definition, experiments result in a set of observable outcomes. |
| AACSB: Communication Accessibility: Keyboard Navigation Blooms: Remember Difficulty: 1 Easy Learning Objective: 05-01 Define the terms probability; experiment; event; and outcome. Topic: What is a Probability? |
| 53. | The probability of two or more events occurring concurrently is called a(n) _________.
The P(A and B and C) is a joint probability. |
| AACSB: Communication Accessibility: Keyboard Navigation Blooms: Remember Difficulty: 1 Easy Learning Objective: 05-04 Calculate probabilities using the rules of multiplication. Topic: Rules of Multiplication to Calculate Probabilities |
| 54. | The probability of an event that is affected by two or more different events is called a(n) ___________.
P(A | B) is a conditional probability indicating that the probability of the event A is affected by event B. |
| AACSB: Communication Accessibility: Keyboard Navigation Blooms: Remember Difficulty: 1 Easy Learning Objective: 05-04 Calculate probabilities using the rules of multiplication. Topic: Rules of Multiplication to Calculate Probabilities |
| 55. | A graphical method used to calculate joint and conditional probabilities is __________.
By definition, the tree diagram is useful for illustrating joint and conditional probabilities. |
| AACSB: Communication Accessibility: Keyboard Navigation Blooms: Remember Difficulty: 1 Easy Learning Objective: 05-04 Calculate probabilities using the rules of multiplication. Topic: Rules of Multiplication to Calculate Probabilities |
| 56. | When an experiment is conducted “without replacement,” __________.
“Without replacement” means that when an individual or object is observed or measured, it is not returned to the population. So on the next selection from the population, each individual or object has a higher probability of selection because the population is now N-1. |
| AACSB: Communication Accessibility: Keyboard Navigation Blooms: Understand Difficulty: 1 Easy Learning Objective: 05-04 Calculate probabilities using the rules of multiplication. Topic: Rules of Multiplication to Calculate Probabilities |
| 57. | If two events are independent, then their joint probability is computed with _________.
The special rule of multiplication is P(A and B) = P(A)P(B) for independent events. |
| AACSB: Communication Accessibility: Keyboard Navigation Blooms: Understand Difficulty: 1 Easy Learning Objective: 05-04 Calculate probabilities using the rules of multiplication. Topic: Rules of Multiplication to Calculate Probabilities |
| 58. | When applying the special rule of addition for mutually exclusive events, the joint probability is _______.
For mutually exclusive events, the joint probability is P(A and B) = 0. |
| AACSB: Communication Accessibility: Keyboard Navigation Blooms: Understand Difficulty: 1 Easy Learning Objective: 05-03 Calculate probabilities using the rules of addition. Topic: Rules of Addition for Computing Probabilities |
| 59. | When an event’s probability depends on the likelihood of another event, the probability is a(n) ___________.
It is a conditional probability, expressed as P(B | A), or the probability of B given A. |
| AACSB: Communication Accessibility: Keyboard Navigation Blooms: Understand Difficulty: 1 Easy Learning Objective: 05-04 Calculate probabilities using the rules of multiplication. Topic: Rules of Multiplication to Calculate Probabilities |
| 60. | 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?
Applying the empirical probability approach, there are 50 maintenance employees out of a total of 2000 employees. The probability is 50/2000 = 0.025. |
| AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-02 Assign probabilities using a classical; empirical; or subjective approach. Topic: Approaches to Assigning Probabilities |
| 61. | 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?
Given mutually exclusive classes, P(maintenance or secretarial) = P(maintenance) + P(secretarial) = 50/2000 + 68/2000 = 0.059. |
| AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-03 Calculate probabilities using the rules of addition. Topic: Rules of Addition for Computing Probabilities |
| 62. | 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?
For mutually exclusive classes, P(management or supervision) = P(management) + P(supervision) = 302/2000 + 120/2000 = 0.21. |
| AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-03 Calculate probabilities using the rules of addition. Topic: Rules of Addition for Computing Probabilities |
| 63. | 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?
Given independence, P(supervision and management) = P(supervision) P(management) = (68/2000)(50/2000) = 0.00085, or rounded to 0.00. |
| AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-04 Calculate probabilities using the rules of multiplication. Topic: Rules of Multiplication to Calculate Probabilities |
| 64. | The process used to calculate the probability of an event given additional information has been obtained through:
|
| AACSB: Communication Accessibility: Keyboard Navigation Blooms: Understand Difficulty: 1 Easy Learning Objective: 05-06 Calculate probabilities using Bayes’ theorem. Topic: Bayes’ Theorem |
| 65. | 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 has excellent potential for advancement?
The events are not independent. P(above average ability and excellent potential) = P(above average ability) P(excellent potential | above average ability) = (300/500) (135/300) = 135/500 = 0.27. |
| AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-05 Compute probabilities using a contingency table. Topic: Contingency Tables |
| 66. | 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?
The events are not independent. P(average ability and good potential) = P(average ability) P(good potential | average ability) = (150/500)(60/150) = 60/500 = 0.12. |
| AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-05 Compute probabilities using a contingency table. Topic: Contingency Tables |
| 67. | 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?
The events are not independent. P(below average ability and fair potential) = P(below average ability) P(fair potential | below average ability) = (60/500)(16/60) = 16/500 = 0.32. |
| AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-05 Compute probabilities using a contingency table. Topic: Contingency Tables |
| 68. | 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?
This is a conditional probability: P(excellent potential | above average ability)(135/300) = .45. There are 300 salespeople who are above average; 135 have excellent potential. |
| AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-05 Compute probabilities using a contingency table. Topic: Contingency Tables |
| 69. | 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?
This is a conditional probability: P(excellent potential | average ability)(45/150) = .30. There are 150 salespeople who are average; 45 have excellent potential. |
| AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-05 Compute probabilities using a contingency table. Topic: Contingency Tables |
| 70. | A study of interior designers’ opinions with respect to the most desirable primary color for executive offices showed the following:
What is the probability that a designer does not prefer red?
Using the complement rule, P(red) = 92/400 = 0.23. Therefore, P(not red) = 1.00 – 0.23 = 0.77. |
| AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-03 Calculate probabilities using the rules of addition. Topic: Rules of Addition for Computing Probabilities |
| 71. | A study of interior designers’ opinions with respect to the most desirable primary color for executive offices showed the following:
What is the probability that a designer does not prefer yellow?
Using the complement rule, P(yellow) = 46/400 = 0.115. Therefore, P(not yellow) = 1.00 – 0.115 = 0.885. |
| AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-03 Calculate probabilities using the rules of addition. Topic: Rules of Addition for Computing Probabilities |
| 72. | A study of interior designers’ opinions with respect to the most desirable primary color for executive offices showed the following:
What is the probability that a designer does not prefer blue?
Using the complement rule, P(blue) = 37/400 = 0.0925. Therefore, P(not blue) = 1.00 – 0.0925 = 0.9075. |
| AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-03 Calculate probabilities using the rules of addition. Topic: Rules of Addition for Computing Probabilities |
| 73. | 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?
Apply the multiplication rule: (0.075)(0.075)(0.075) = 0.0004219. |
| AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-04 Calculate probabilities using the rules of multiplication. Topic: Rules of Multiplication to Calculate Probabilities |
| 74. | 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?
Apply the multiplication rule: (0.90)(0.90)(0.90) = 0.729. |
| AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-04 Calculate probabilities using the rules of multiplication. Topic: Rules of Multiplication to Calculate Probabilities |
| 75. | 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?
|
| AACSB: Analytic Accessibility: Keyboard Navigation Blooms: Apply Difficulty: 3 Hard Learning Objective: 05-06 Calculate probabilities using Bayes’ theorem. Topic: Bayes’ Theorem |
| 76. | Using the terminology of Bayes’ theorem, a posterior probability can also be defined as:
|
| AACSB: Communication Accessibility: Keyboard Navigation Blooms: Understand Difficulty: 1 Easy Learning Objective: 05-06 Calculate probabilities using Bayes’ theorem. Topic: Bayes’ Theorem |
| 77. | If A and B are mutually exclusive events with P(A) = 0.2 and P(B) = 0.6, then P(A or B) = _____.
Use formula [5-4]: P(A or B) = P(A) + P(B) – P(A and B). Since the events are mutually exclusive, P(A and B) = 0 and P(A or B) = (0.20) + (0.60) = 0.80. |
| AACSB: Analytic Accessibility: Keyboard Navigation Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-03 Calculate probabilities using the rules of addition. Topic: Rules of Addition for Computing Probabilities |
| 78. | If P(A) = 0.62, P(B) = 0.47, and P(A or B) = 0.88, then P(A and B) = _____.
Use formula [5-4]: P(A or B) = P(A) + P(B) – P(A and B). Rearrange formula [5-4]: P(A and B) = P(A) + P(B) – P(A or B) = 0.62 + 0.47 – 0.88 = 0.21. P(A and B) = 0.21. |
| AACSB: Analytic Accessibility: Keyboard Navigation Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-03 Calculate probabilities using the rules of addition. Topic: Rules of Addition for Computing Probabilities |
| 79. | A method of assigning probabilities based upon judgment, opinions, and available information is referred to as the:
|
| AACSB: Communication Accessibility: Keyboard Navigation Blooms: Remember Difficulty: 1 Easy Learning Objective: 05-02 Assign probabilities using a classical; empirical; or subjective approach. Topic: Approaches to Assigning Probabilities |
| 80. | Your favorite soccer team has two remaining matches to complete the season. The possible outcomes of a soccer match are win, lose, or tie. What is the possible number of outcomes for the season?
Use the tree diagram to determine the possible outcomes, which are: {W,W},{W,L},{W,T},{L,W},{L,L},{L,T},{T,W},{T,L},{T,T}. There are 9 possible outcomes. |
| AACSB: Analytic Accessibility: Keyboard Navigation Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-07 Determine the number of outcomes using principles of counting. Topic: Principles of Counting |
Fill in the Blank Questions
| 81. | Complete the following analogy: An experiment relates to outcome, as the role of a die relates to _____.
any one value between 1 and 6 The role of a die is an experiment with six possible outcomes. |
| AACSB: Communication Blooms: Understand Difficulty: 2 Medium Learning Objective: 05-01 Define the terms probability; experiment; event; and outcome. Topic: What is a Probability? |
| 82. | If a set of outcomes is collectively exhaustive and mutually exclusive, the sum of the probabilities equals __________.
1 By definition, if the set of outcomes covers all possible experimental outcomes, and are mutually exclusive, then the probabilities of the outcomes must sum to 1. |
| AACSB: Communication Blooms: Understand Difficulty: 2 Medium Learning Objective: 05-02 Assign probabilities using a classical; empirical; or subjective approach. Topic: Approaches to Assigning Probabilities |
| 83. | When the special rule of multiplication is used, the events must be _______________.
independent The special rule of multiplication is P(A and B) = P(A)P(B). There is no conditional probability because the events are independent. |
| AACSB: Communication Blooms: Understand Difficulty: 2 Medium Learning Objective: 05-04 Calculate probabilities using the rules of multiplication. Topic: Rules of Multiplication to Calculate Probabilities |
| 84. | When the special rule of addition is used, the events must be _______________.
mutually exclusive The special rule of addition is P(A or B) = P(A) + P(B). Note that the rule does not include the joint probability P(A and B), because A and B are mutually exclusive, or the events A and B do not have any outcomes in common. |
| AACSB: Communication Blooms: Understand Difficulty: 2 Medium Learning Objective: 05-03 Calculate probabilities using the rules of addition. Topic: Rules of Addition for Computing Probabilities |
| 85. | The probability of selecting a professor who is male and has a master’s degree is called a ______________.
joint probability This is restated as P(male and master’s degree) = P(male)P(master’s degree), assuming that the two events are independent. |
| AACSB: Communication Blooms: Understand Difficulty: 2 Medium Learning Objective: 05-04 Calculate probabilities using the rules of multiplication. Topic: Rules of Multiplication to Calculate Probabilities |
| 86. | To summarize the frequencies of two nominal or ordinal variables and compute conditional probabilities, a ___________ can be used.
contingency table A contingency table is used to summarize the frequencies of two nominal or ordinal variables. These frequencies can then be used to compute conditional probabilities. |
| AACSB: Communication Blooms: Understand Difficulty: 2 Medium Learning Objective: 05-05 Compute probabilities using a contingency table. Topic: Contingency Tables |
| 87. | The joint probability of two events that are not independent, P(A and B), is computed as _______________.
P(A and B) = P(A) P(B|A) By definition, P(A and B) = P(A) P(B|A). |
| AACSB: Communication Blooms: Remember Difficulty: 2 Medium Learning Objective: 05-04 Calculate probabilities using the rules of multiplication. Topic: Rules of Multiplication to Calculate Probabilities |
| 88. | The probability that a flipped coin will show heads on four consecutive flips is _______________.
0.0625 Based on the classical approach, P(head) = 0.5. The probability of heads on four independent flips is (.5)(.5)(.5)(.5) = 0.0625. |
| AACSB: Analytic Blooms: Understand Difficulty: 2 Medium Learning Objective: 05-04 Calculate probabilities using the rules of multiplication. Topic: Rules of Multiplication to Calculate Probabilities |
| 89. | In a tree diagram that illustrates the joint probabilities for a probability problem, the sum of all the joint probabilities must equal _______________.
1 A tree diagram shows all possible, mutually exclusive outcomes of an experiment. Therefore, the sum of the joint probabilities must equal one. |
| AACSB: Reflective Thinking Blooms: Analyze Difficulty: 3 Hard Learning Objective: 05-03 Calculate probabilities using the rules of addition. Topic: Rules of Addition for Computing Probabilities |
| 90. | Suppose you toss a coin four times and get heads four times (no tails). The probability that heads will appear on the next toss of the coin is ____.
0.5 Based on the classical approach, P(heads) = 0.5. The outcomes of the experiment are independent, so the probability of heads on any single toss is 0.5. |
| AACSB: Communication Blooms: Understand Difficulty: 2 Medium Learning Objective: 05-02 Assign probabilities using a classical; empirical; or subjective approach. Topic: Approaches to Assigning Probabilities |
| 91. | The _________ approach to probability is based on a person’s belief, opinion, or judgment.
subjective A person can subjectively assign probabilities based on belief, opinion, or judgment. |
| AACSB: Communication Blooms: Remember Difficulty: 2 Medium Learning Objective: 05-02 Assign probabilities using a classical; empirical; or subjective approach. Topic: Approaches to Assigning Probabilities |
| 92. | If there are five vacant parking places and five automobiles arrive at the same time, the number of different ways they can park is ____.
120 Using the multiplication rule: (5)(4)(3)(2)(1) = 120. |
| AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-07 Determine the number of outcomes using principles of counting. Topic: Principles of Counting |
| 93. | A collection of one or more possible outcomes of an experiment is called a(n) ___________.
event By definition, a set of one or more experimental outcomes is called an event. |
| AACSB: Communication Blooms: Remember Difficulty: 2 Medium Learning Objective: 05-01 Define the terms probability; experiment; event; and outcome. Topic: What is a Probability? |
| 94. | A new computer game has been developed and 80 veteran game players will test its market potential. If 60 players liked the game, the probability that any veteran game player will like the new computer game is ______.
0.75 Applying the empirical approach to probability, 60/80 = 0.75. |
| AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-02 Assign probabilities using a classical; empirical; or subjective approach. Topic: Approaches to Assigning Probabilities |
| 95. | One card will be randomly selected from a standard 52-card deck. The probability that it will be the jack of hearts is ____.
1/52 or 0.0192 Applying the empirical approach to probability, there is one jack of hearts in a deck of 52 cards. 1/52 = 0.0192. |
| AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-02 Assign probabilities using a classical; empirical; or subjective approach. Topic: Approaches to Assigning Probabilities |
| 96. | The theorem that applies additional information to revise probabilities is called ________.
Bayes’ theorem |
| AACSB: Communication Blooms: Remember Difficulty: 1 Easy Learning Objective: 05-06 Calculate probabilities using Bayes’ theorem. Topic: Bayes’ Theorem |
| 97. | A probability is calculated by dividing the number of desired outcomes by the total number of occurrences. This approach to probability is called __________.
empirical approach By definition, when an experiment is observed and outcomes are counted to determine probabilities, the empirical approach to probability is applied. |
| AACSB: Communication Blooms: Remember Difficulty: 2 Medium Learning Objective: 05-02 Assign probabilities using a classical; empirical; or subjective approach. Topic: Approaches to Assigning Probabilities |
| 98. | The probability that a one, two, or six will appear face up on the throw of one die is _____.
0.5 On a single die, there are six possible outcomes—1, 2, 3, 4, 5, 6—each having a 1/6, or 0.1667, probability. The probability of the event that one of the three outcomes occur is (one or two or six) = (1/6) + (1/6) + (1/6) = 3/6 = ½ = 0.5. |
| AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-02 Assign probabilities using a classical; empirical; or subjective approach. Topic: Approaches to Assigning Probabilities |
| 99. | A measured or observed activity is called a(n) ___________.
experiment By definition, an experiment is an observed or empirical process. |
| AACSB: Communication Blooms: Remember Difficulty: 2 Medium Learning Objective: 05-01 Define the terms probability; experiment; event; and outcome. Topic: What is a Probability? |
| 100. | The particular result of an experiment is called a(n) _________.
outcome By definition, we observe experimental outcomes. |
| AACSB: Communication Blooms: Remember Difficulty: 2 Medium Learning Objective: 05-01 Define the terms probability; experiment; event; and outcome. Topic: What is a Probability? |
| 101. | A collection of one or more basic outcomes is called a(n) _________.
event By definition, an event is a set of one or more experimental outcomes. |
| AACSB: Communication Blooms: Remember Difficulty: 2 Medium Learning Objective: 05-01 Define the terms probability; experiment; event; and outcome. Topic: What is a Probability? |
| 102. | To apply the special rule of addition, the events must be _________.
mutually exclusive If experimental events have no outcomes in common, then they are mutually exclusive and the joint probability of any events is zero. Therefore, we can apply the special rule of addition. |
| AACSB: Communication Blooms: Understand Difficulty: 2 Medium Learning Objective: 05-03 Calculate probabilities using the rules of addition. Topic: Rules of Addition for Computing Probabilities |
| 103. | Two events are called _________ when the occurrence of one event does not affect the occurrence of the other event.
independent Independence occurs when there are no conditional events. |
| AACSB: Communication Blooms: Remember Difficulty: 2 Medium Learning Objective: 05-04 Calculate probabilities using the rules of multiplication. Topic: Rules of Multiplication to Calculate Probabilities |
| 104. | When the order of a set of objects selected from a single group is important, this is called ________.
permutation By definition, a permutation is a set of ordered objects that define an experimental event. For example, the event, AB, is different from the event, BA. |
| AACSB: Communication Blooms: Remember Difficulty: 2 Medium Learning Objective: 05-07 Determine the number of outcomes using principles of counting. Topic: Principles of Counting |
| 105. | A ________ is useful when applying Bayes’ theorem.
tree diagram |
| AACSB: Communication Blooms: Remember Difficulty: 1 Easy Learning Objective: 05-06 Calculate probabilities using Bayes’ theorem. Topic: Bayes’ Theorem |
Essay Questions
| 106. | 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% Feedback: There are 100 total people surveyed; 35 favored orange. Applying the empirical probability approach, 35/100 = 0.35. |
| AACSB: Analytic Blooms: Apply Difficulty: 1 Easy Learning Objective: 05-02 Assign probabilities using a classical; empirical; or subjective approach. Topic: Approaches to Assigning Probabilities |
| 107. | 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% Feedback: Applying the empirical probability approach, of 100 total people surveyed, 35 favored orange, and 25 favored lime. Applying the special rule of addition P(orange or lime) = 35/100 + 25/100 = 60/100 = 0.60. |
| AACSB: Analytic Blooms: Apply Difficulty: 1 Easy Learning Objective: 05-02 Assign probabilities using a classical; empirical; or subjective approach. Topic: Approaches to Assigning Probabilities |
| 108. | 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 person’s response to the question Feedback: An outcome is the response of any one person to the survey. |
| AACSB: Reflective Thinking Blooms: Remember Difficulty: 1 Easy Learning Objective: 05-01 Define the terms probability; experiment; event; and outcome. Topic: What is a Probability? |
| 109. | 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% Feedback: Applying the empirical probability approach, of 2000 total people, 200 were rated excellent, 1700 were rated good. Applying the special rule of addition P(good or excellent) = 200/2000 + 1700/2000 = 1900/2000 = 0.95. |
| AACSB: Analytic Blooms: Apply Difficulty: 1 Easy Learning Objective: 05-03 Calculate probabilities using the rules of addition. Topic: Rules of Addition for Computing Probabilities |
| 110. | In flipping a fair coin, what is the probability of either heads or tails on one toss?
1.0 or 100% Feedback: The P(heads or tails) = P(heads) + P(tails) = 0.5 + 0.5 = 1.0. Also, the sum of the probabilities of events that are mutually exclusive and collectively exhaustive is always equal to one. |
| AACSB: Analytic Blooms: Apply Difficulty: 1 Easy Learning Objective: 05-03 Calculate probabilities using the rules of addition. Topic: Rules of Addition for Computing Probabilities |
| 111. | In flipping a fair coin, what is the probability of both heads and tails on one toss?
0.00 or 0% Feedback: These are mutually exclusive events, so the joint probability of heads and tails on one toss is zero. The event is not even possible. |
| AACSB: Analytic Blooms: Apply Difficulty: 1 Easy Learning Objective: 05-03 Calculate probabilities using the rules of addition. Topic: Rules of Addition for Computing Probabilities |
| 112. | In flipping a fair coin, what is the probability of heads and tails on two tosses?
0.50 or 50% Feedback: Based on the multiplication rule, there are four possible outcomes: HH, HT, TH, and TT. So there are two out of four possible ways for the event to occur. Thus, the probability is 0.5. |
| AACSB: Analytic Blooms: Apply Difficulty: 1 Easy Learning Objective: 05-04 Calculate probabilities using the rules of multiplication. Topic: Rules of Multiplication to Calculate Probabilities |
| 113. | Airlines monitor the causes of flights arriving late. A total of 75% of flights are late because of weather, while 35% of flights are late because of ground operations. A full 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 Feedback: A joint probability is P(A and B) = P(A) P(B). The problem provides the answer: 10% of flights are late because of weather AND ground operations. |
| AACSB: Reflective Thinking Blooms: Understand Difficulty: 1 Easy Learning Objective: 05-04 Calculate probabilities using the rules of multiplication. Topic: Rules of Multiplication to Calculate Probabilities |
| 114. | Airlines monitor the causes of flights arriving late. A total of 75% of flights are late because of weather, while 35% of flights are late because of ground operations. A full 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 Feedback: The general rule of addition is P(A or B) = P(A) + P(B) – P(A and B) or P(weather or ground operations) = .75 + .35 – .15 = 0.95. |
| AACSB: Analytic Blooms: Apply Difficulty: 1 Easy Learning Objective: 05-03 Calculate probabilities using the rules of addition. Topic: Rules of Addition for Computing Probabilities |
| 115. | 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 Feedback: A joint probability is P(A and B) = P(A)P(B) = (.60)(.45) = .27. |
| AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-04 Calculate probabilities using the rules of multiplication. Topic: Rules of Multiplication to Calculate Probabilities |
| 116. | In a deck of 52 cards, what is the probability of selecting two kings from the deck without replacement?
0.0045 Feedback: Without replacement requires the use of a conditional probability. On the first draw, the probability of a king is 4/52. Given the card is not returned to the deck, the probability of a second king is 3/51. The final answer is a joint probability of the two events or (4/52)(3/52) = 0.0045. |
| AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-04 Calculate probabilities using the rules of multiplication. Topic: Rules of Multiplication to Calculate Probabilities |
| 117. | 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 Feedback: The joint probability: P(Female and Dissatisfied) = P(Female) P(Dissatisfied) = (22/100) = 0.22. |
| AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 05-05 Compute probabilities using a contingency table. Topic: Contingency Tables |
| 118. | 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 Feedback: Applying the general rule of addition, P(male or dissatisfied) = P(male) + P(dissatisfied) – P(male and dissatisfied) = (.6) + (.55) – (.33) = 0.82. |
| AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 05-05 Compute probabilities using a contingency table. Topic: Contingency Tables |
| 119. | 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 Feedback: Applying conditional probabilities, P(Satisfied | male) = 27/60 = 0.45. |
| AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 05-05 Compute probabilities using a contingency table. Topic: Contingency Tables |
| 120. | 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 Feedback: Based on frequencies, there are 15 of the total of 200 who like white cell phones, or a probability of 0.075 of randomly selecting a person who likes white cell phones. |
| AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-03 Calculate probabilities using the rules of addition. Topic: Rules of Addition for Computing Probabilities |
| 121. | 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 Feedback: Based on the frequencies, 70 of 200 people favor black and 60 or 200 people favor orange. Applying the special rule of addition, the P(black or orange) = (70/200) + (60/200) = 130/200 = 0.65. |
| AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-03 Calculate probabilities using the rules of addition. Topic: Rules of Addition for Computing Probabilities |
| 122. | 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 Feedback: This is a conditional probability P(orange | age is less than 21). Of the 100 people who are less then 21 years old, 35 prefer orange. Therefore, the conditional probability is 0.35. |
| AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-04 Calculate probabilities using the rules of multiplication. Topic: Rules of Multiplication to Calculate Probabilities |
| 123. | 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 Feedback: This is a conditional probability P(black | age is 21 or greater). Of the 100 people who are 21 or more years old, 50 prefer black. Therefore, the conditional probability is 0.50. |
| AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-04 Calculate probabilities using the rules of multiplication. Topic: Rules of Multiplication to Calculate Probabilities |
| 124. | 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 red is the favorite color, given that the person’s age is 21 or older? 0.05 Feedback: This is a conditional probability P(red | age is 21 or greater). Of the 100 people who are 21 or more years old, 5 prefer red. Therefore, the conditional probability is 0.05. |
| AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-04 Calculate probabilities using the rules of multiplication. Topic: Rules of Multiplication to Calculate Probabilities |
| 125. | 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 Feedback: Applying the special rule of addition for ages 21 or greater, the probabilities for black, lime, and orange are 50/100, 15/100, and 25/100. The sum of the probabilities is 90/100 or 0.90. |
| AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-05 Compute probabilities using a contingency table. Topic: Contingency Tables |
| 126. | 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 in a game, how many outcomes are possible?
36 Feedback: Using the multiplication rule, each die has six possible outcomes. So (6)(6) = 36 possible outcomes. |
| AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-07 Determine the number of outcomes using principles of counting. Topic: Principles of Counting |
| 127. | 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 two students. How many different samples are possible?
45 Feedback: Applying the combination rule, (n!)/(r!(n – r)!) = 10!/(2!8!) = 90/2 = 45. |
| AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-07 Determine the number of outcomes using principles of counting. Topic: Principles of Counting |
| 128. | A student organization of 10 wants to select a president, a vice-president, and a treasurer. How many different leadership assignments are possible?
720 Feedback: Applying the multiplication formula: 10*9*8 = 720 different leadership assignments. |
| AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-07 Determine the number of outcomes using principles of counting. Topic: Principles of Counting |
| 129. | Draw a Venn diagram showing the probability for two mutually exclusive events and also draw 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 Blooms: Analyze Difficulty: 3 Hard Learning Objective: 05-03 Calculate probabilities using the rules of addition. Topic: Rules of Addition for Computing Probabilities |
| 130. | 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 Blooms: Understand Difficulty: 3 Hard Learning Objective: 05-02 Assign probabilities using a classical; empirical; or subjective approach. Topic: Approaches to Assigning Probabilities |
| 131. | 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, 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 Blooms: Understand Difficulty: 3 Hard Learning Objective: 05-07 Determine the number of outcomes using principles of counting. Topic: Principles of Counting |
| 132. | 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 Blooms: Understand Difficulty: 3 Hard Learning Objective: 05-04 Calculate probabilities using the rules of multiplication. Topic: Rules of Multiplication to Calculate Probabilities |
| 133. | A cell phone salesperson has kept records on the customers who visited his store. Forty percent 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 A1 represent the event that a customer is a female, A2 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 Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-06 Calculate probabilities using Bayes’ theorem. Topic: Bayes’ Theorem |
| 134. | A cell phone salesperson has kept records on the customers who visited his store. Forty percent 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 A1 represent the event that a customer is a female, A2 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 Blooms: Apply Difficulty: 2 Medium Learning Objective: 05-06 Calculate probabilities using Bayes’ theorem. Topic: Bayes’ Theorem |
Original price was: $30.00.$20.00Current price is: $20.00.
Original price was: $30.00.$20.00Current price is: $20.00.
Original price was: $30.00.$20.00Current price is: $20.00.
Original price was: $30.00.$20.00Current price is: $20.00.
Original price was: $30.00.$20.00Current price is: $20.00.
Original price was: $30.00.$20.00Current price is: $20.00.
