Basic Probability 87 CHAPTER 4: BASIC PROBABILITY 1. If two events are collectively exhaustive, what is the probability that one or the other occurs? a) 0 b) 0.50 c) 1.00 d) Cannot be determined from the information given. ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: collectively exhaustive 2. If two events are collectively exhaustive, what is the probability that both occur at the same time? a) 0 b) 0.50 c) 1.00 d) Cannot be determined from the information given. ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: collectively exhaustive, mutually exclusive EXPLANATION: We do not know if they are mutually exclusive. 3. If two events are mutually exclusive, what is the probability that one or the other occurs? a) 0 b) 0.50 c) 1.00 d) Cannot be determined from the information given. ANSWER: d TYPE: MC DIFFICULTY: moderate KEYWORDS: collectively exhaustive, mutually exclusive EXPLANATION: We do not know if they are collectively exhaustive. 4. If two events are mutually exclusive, what is the probability that both occur at the same time? a) 0 b) 0.50 c) 1.00 d) Cannot be determined from the information given. ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: mutually exclusive 88 Basic Probability 5. If two events are mutually exclusive and collectively exhaustive, what is the probability that both occur? a) 0 b) 0.50 c) 1.00 d) Cannot be determined from the information given. ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: collective exhaustive, mutually exclusive 6. If two events are mutually exclusive and collectively exhaustive, what is the probability that one or the other occurs? a) 0 b) 0.50 c) 1.00 a) Cannot be determined from the information given. ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: collectively exhaustive, mutually exclusive 7. If events A and B are mutually exclusive and collectively exhaustive, what is the probability that event A occurs? a) 0 b) 0.50 c) 1.00 a) Cannot be determined from the information given. ANSWER: d TYPE: MC DIFFICULTY: moderate KEYWORDS: collectively exhaustive, mutually exclusive EXPLANATION: We do not know if they are equally likely events. 8. If two equally likely events A and B are mutually exclusive and collectively exhaustive, what is the probability that event A occurs? a) 0 b) 0.50 c) 1.00 a) Cannot be determined from the information given. ANSWER: b TYPE: MC DIFFICULTY: easy KEYWORDS: collectively exhaustive, mutually exclusive Basic Probability 89 9. If two equally likely events A and B are mutually exclusive, what is the probability that event A occurs? a) 0 b) 0.50 c) 1.00 a) Cannot be determined from the information given. ANSWER: d TYPE: MC DIFFICULTY: moderate KEYWORDS: collectively exhaustive, mutually exclusive EXPLANATION: We do not know if they are collectively exhaustive. 10. If two equally likely events A and B are collectively exhaustive, what is the probability that event A occurs? a) 0 b) 0.50 c) 1.00 d) Cannot be determined from the information given. ANSWER: d TYPE: MC DIFFICULTY: moderate KEYWORDS: collectively exhaustive, mutually exclusive EXPLANATION: We do not know if they are mutually exclusive. 11. Selection of raffle tickets from a large bowl is an example of a) sampling with replacement. b) sampling without replacement. c) subjective probability. d) none of the above ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: sampling with replacement, sampling without replacement 12. If two events are independent, what is the probability that they both occur? a) 0 b) 0.50 c) 1.00 d) Cannot be determined from the information given. ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: statistical independence 90 Basic Probability 13. If the outcome of event A is not affected by event B, then events A and B are said to be a) mutually exclusive. b) statistically independent. c) collectively exhaustive. d) none of the above ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: statistical independence 14. If event A and event B cannot occur at the same time, then events A and B are said to be a) mutually exclusive. b) statistically independent. c) collectively exhaustive. d) none of the above ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: mutually exclusive 15. If either event A or event B must occur, then events A and B are said to be a) mutually exclusive. b) statistically independent. c) collectively exhaustive. d) none of the above ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: collectively exhaustive 16. The collection of all possible events is called a) a simple probability. b) a sample space. c) a joint probability. d) the null set. ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: sample space Basic Probability 91 17. All the events in the sample space that are not part of the specified event are called a) simple events. b) joint events. c) the sample space. d) the complement of the event. ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: sample space, complement 18. Simple probability is also called a) marginal probability. b) joint probability. c) conditional probability. d) Bayes' theorem. ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: marginal probability 19. When using the general multiplication rule, P(A and B) is equal to a) P(A|B)P(B). b) P(A)P(B). c) P(B)/P(A). d) P(A)/P(B). ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: multiplication rule 20. A business venture can result in the following outcomes (with their corresponding chance of occurring in parentheses): Highly Successful (10%), Successful (25%), Break Even (25%), Disappointing (20%), and Highly Disappointing (?). If these are the only outcomes possible for the business venture, what is the chance that the business venture will be considered Highly Disappointing? a) 10% b) 15% c) 20% d) 25% ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: marginal probability 92 Basic Probability 21. A recent survey of banks revealed the following distribution for the interest rate being charged on a home loan (based on a 30-year mortgage with a 10% down payment). Interest Rate Probability 7.0% 0.12 7.5% 0.23 8.0% 0.24 8.5% 0.35 > 8.5% 0.06 If a bank is selected at random from this distribution, what is the chance that the interest rate charged on a home loan will exceed 8.0%? a) 0.06 b) 0.41 c) 0.59 d) 1.00 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: marginal probability, addition rule 22. The employees of a company were surveyed on questions regarding their educational background and marital status. Of the 600 employees, 400 had college degrees, 100 were single, and 60 were single college graduates. The probability that an employee of the company is single or has a college degree is: a) 0.10. b) 0.25. c) 0.667. d) 0.733. ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: addition rule 23. The employees of a company were surveyed on questions regarding their educational background and marital status. Of the 600 employees, 400 had college degrees, 100 were single, and 60 were single college graduates. The probability that an employee of the company is married and has a college degree is: a) 40/600. b) 340/600. c) 400/600. d) 500/600. ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: joint probability Basic Probability 93 24. The employees of a company were surveyed on questions regarding their educational background and marital status. Of the 600 employees, 400 had college degrees, 100 were single, and 60 were single college graduates. The probability that an employee of the company does not have a college degree is: a) 0.10. b) 0.33. c) 0.67. d) 0.75. ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: complement 25. The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. The probability that both house sales and interest rates will increase during the next 6 months is: a) 0.10. b) 0.185. c) 0.705. d) 0.90. ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: joint probability 26. The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. The probability that neither house sales nor interest rates will increase during the next 6 months is: a) 0.11. b) 0.195. c) 0.89. d) 0.90. ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: joint probability, complement 94 Basic Probability 27. The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. The probability that house sales will increase but interest rates will not during the next 6 months is: a) 0.065. b) 0.15. c) 0.51. d) 0.89. ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: joint probability, complement 28. The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. The events of increase in house sales and increase in interest rates in the next 6 months are a) statistically independent. b) mutually exclusive. c) collectively exhaustive. d) none of the above ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: joint probability, statistical independence EXPLANATION: They are not statistically independent. 29. The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. The events of increase in house sales and no increase in house sales in the next 6 months are a) statistically independent. b) mutually exclusive. c) collectively exhaustive. d) (b) and (c) ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: mutually exclusive, collectively exhaustive, complement Basic Probability 95 30. The probability that a new advertising campaign will increase sales is assessed as being 0.80. The probability that the cost of developing the new ad campaign can be kept within the original budget allocation is 0.40. Assuming that the two events are independent, the probability that the cost is kept within budget and the campaign will increase sales is: a) 0.20. b) 0.32. c) 0.40. d) 0.88. ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: statistical independence, joint probability, multiplication rule 31. The probability that a new advertising campaign will increase sales is assessed as being 0.80. The probability that the cost of developing the new ad campaign can be kept within the original budget allocation is 0.40. Assuming that the two events are independent, the probability that the cost is kept within budget or the campaign will increase sales is: a) 0.20. b) 0.32. c) 0.68. d) 0.88. ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: statistical independence, multiplication rule, addition rule 32. The probability that a new advertising campaign will increase sales is assessed as being 0.80. The probability that the cost of developing the new ad campaign can be kept within the original budget allocation is 0.40. Assuming that the two events are independent, the probability that the cost is not kept within budget or the campaign will not increase sales is: a) 0.12. b) 0.32. c) 0.68. d) 0.88. ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: statistical independence, multiplication rule, addition rule, complement 96 Basic Probability 33. The probability that a new advertising campaign will increase sales is assessed as being 0.80. The probability that the cost of developing the new ad campaign can be kept within the original budget allocation is 0.40. Assuming that the two events are independent, the probability that neither the cost is kept within budget nor the campaign will increase sales is: a) 0.12. b) 0.32. c) 0.68. d) 0.88. ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: statistical independence, multiplication rule, joint probability, complement 34. According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $25,000 is 80%. Of the households surveyed, 60% had incomes over $25,000 and 70% had 2 cars. The probability that the residents of a household own 2 cars and have an income over $25,000 a year is: a) 0.12. b) 0.18. c) 0.22. d) 0.48. ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: joint probability, conditional probability 35. According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $25,000 is 80%. Of the households surveyed, 60% had incomes over $25,000 and 70% had 2 cars. The probability that the residents of a household do not own 2 cars and have an income over $25,000 a year is: a) 0.12. b) 0.18. c) 0.22. d) 0.48. ANSWER: a TYPE: MC DIFFICULTY: Difficult KEYWORDS: joint probability, complement, multiplication rule, conditional probability Basic Probability 97 36. According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $25,000 is 80%. Of the households surveyed, 60% had incomes over $25,000 and 70% had 2 cars. The probability that the residents of a household own 2 cars and have an income less than or equal to $25,000 a year is: a) 0.12. b) 0.18. c) 0.22. d) 0.48. ANSWER: c TYPE: MC DIFFICULTY: Difficult KEYWORDS: joint probability, complement, multiplication rule, conditional probability 37. According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $25,000 is 80%. Of the households surveyed, 60% had incomes over $25,000 and 70% had 2 cars. The probability that annual household income is over $25,000 if the residents of a household own 2 cars is: a) 0.42. b) 0.48. c) 0.50. d) 0.69. ANSWER: d TYPE: MC DIFFICULTY: Difficult KEYWORDS: conditional probability, Bayes' theorem 38. According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $25,000 is 80%. Of the households surveyed, 60% had incomes over $25,000 and 70% had 2 cars. The probability that annual household income is over $25,000 if the residents of a household do not own 2 cars is: a) 0.12. b) 0.18. c) 0.40. d) 0.70. ANSWER: c TYPE: MC DIFFICULTY: Difficult KEYWORDS: conditional probability, complement, Bayes' theorem 98 Basic Probability 39. According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $25,000 is 80%. Of the households surveyed, 60% had incomes over $25,000 and 70% had 2 cars. The probability that the residents do not own 2 cars if annual household income is not over $25,000 is: a) 0.12. b) 0.18. c) 0.45. d) 0.70. ANSWER: c TYPE: MC DIFFICULTY: Difficult KEYWORDS: conditional probability, complement 40. A company has 2 machines that produce widgets. An older machine produces 23% defective widgets, while the new machine produces only 8% defective widgets. In addition, the new machine produces 3 times as many widgets as the older machine does. Given that a widget was produced by the new machine, what is the probability it is not defective? a) 0.06 b) 0.50 c) 0.92 d) 0.94 ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: conditional probability, complement 41. A company has 2 machines that produce widgets. An older machine produces 23% defective widgets, while the new machine produces only 8% defective widgets. In addition, the new machine produces 3 times as many widgets as the older machine does. What is the probability that a randomly chosen widget produced by the company is defective? a) 0.078 b) 0.1175 c) 0.156 d) 0.310 ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: marginal probability Basic Probability 99 42. A company has 2 machines that produce widgets. An older machine produces 23% defective widgets, while the new machine produces only 8% defective widgets. In addition, the new machine produces 3 times as many widgets as the older machine does. Given that a randomly chosen widget was tested and found to be defective, what is the probability it was produced by the new machine? a) b) c) d) 0.08 0.15 0.489 0.511 ANSWER: d TYPE: MC DIFFICULTY: Difficult KEYWORDS: conditional probability, Bayes' theorem TABLE 4-1 Mothers Against Drunk Driving is a very visible group whose main focus is to educate the public about the harm caused by drunk drivers. A study was recently done that emphasized the problem we all face with drinking and driving. Four hundred accidents that occurred on a Saturday night were analyzed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident. The numbers are shown below: Did alcohol play a role? Yes No Totals Number of Vehicles Involved 1 2 3 50 100 20 25 175 30 75 275 50 Totals 170 230 400 43. Referring to Table 4-1, what proportion of accidents involved more than one vehicle? a) 50/400 b) 75/400 c) 275/400 d) 325/400 ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, empirical classical probability, addition rule 100 Basic Probability 44. Referring to Table 4-1, what proportion of accidents involved alcohol and a single vehicle? a) 25/400 b) 50/400 c) 195/400 d) 245/400 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, empirical classical probability, joint probability 45. Referring to Table 4-1, what proportion of accidents involved alcohol or a single vehicle? a) 25/400 b) 50/400 c) 195/400 d) 245/400 ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, empirical classical probability, addition rule 46. Referring to Table 4-1, given alcohol was involved, what proportion of accidents involved a single vehicle? a) 50/75 b) 50/170 c) 120/170 d) 120/400 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, empirical classical probability, marginal probability 47. Referring to Table 4-1, given that multiple vehicles were involved, what proportion of accidents involved alcohol? a) 120/170 b) 120/230 c) 120/325 d) 120/400 ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, empirical classical probability, conditional probability, addition rule Basic Probability 101 48. Referring to Table 4-1, given that 3 vehicles were involved, what proportion of accidents involved alcohol? a) 20/30 b) 20/50 c) 20/170 d) 20/400 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, empirical classical probability, conditional probability 49. Referring to Table 4-1, given that alcohol was not involved, what proportion of the accidents were single vehicle? a) 50/75 b) 25/230 c) 50/170 d) 25/75 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, empirical classical probability, conditional probability, complement 50. Referring to Table 4-1, given that alcohol was not involved, what proportion of the accidents were multiple vehicle? a) 50/170 b) 120/170 c) 205/230 d) 25/230 ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, empirical classical probability, conditional probability, complement 102 Basic Probability TABLE 4-2 An alcohol awareness task force at a Big Ten university sampled 200 students after the midterm to ask them whether they went bar hopping the weekend before the midterm or spent the weekend studying, and whether they did well or poorly on the midterm. The following result was obtained. Studying for Exam Went Bar Hopping Did Well on Midterm 80 30 Did Poorly on Midterm 20 70 51. Referring to Table 4-2, what is the probability that a randomly selected student who went bar hopping will do well on the midterm? a. 30/100 b. 30/110 c. 30/200 d. (100/200)*(110/200) ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, empirical classical probability, conditional probability 52. Referring to Table 4-2, what is the probability that a randomly selected student did well on the midterm or went bar hopping the weekend before the midterm? a) 30/200 b) (80+30)/200 c) (30+70)/200 d) (80+30+70)/200 ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, empirical classical probability, addition rule 53. Referring to Table 4-2, what is the probability that a randomly selected student did well on the midterm and also went bar hopping the weekend before the midterm? a) 30/200 b) (80+30)/200 c) (30+70)/200 d) (80+30+70)/200 ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, empirical classical probability, joint probability Basic Probability 103 54. Referring to Table 4-2, the events "Did Well on Midterm" and "Studying for Exam" are a) statistically dependent. b) mutually exclusive. c) collective exhaustive. d) none of the above ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, empirical classical probability, statistical independence, joint probability 55. Referring to Table 4-2, the events "Did Well on Midterm" and "Studying for Exam" are a) not statistically dependent. b) not mutually exclusive. c) collective exhaustive. d) none of the above ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, empirical classical probability, mutually exclusive, joint probability 56. Referring to Table 4-2, the events "Did Well on Midterm" and "Did Poorly on Midterm" are a) statistically dependent. b) mutually exclusive. c) collective exhaustive. d) all of the above ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, empirical classical probability, statistical independence, mutually exclusive, collective exhaustive, joint probability 57. True or False: When A and B are mutually exclusive, P(A or B) can be found by adding P(A) and P(B). ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: mutually exclusive, addition rule 58. True or False: The collection of all the possible events is called a sample space. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: sample space 59. True or False: If A and B cannot occur at the same time, they are called mutually exclusive. 104 Basic Probability ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: mutually exclusive 60. True or False: If either A or B must occur, they are called mutually exclusive. ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: mutually exclusive, collective exhaustive 61. True or False: If either A or B must occur, they are called collectively exhaustive. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: collective exhaustive 62. True or False: If P(A) = 0.4 and P(B) = 0.6, then A and B must be collectively exhaustive. ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: collective exhaustive, mutually exclusive 63. True or False: If P(A) = 0.4 and P(B) = 0.6, then A and B must be mutually exclusive. ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: mutually exclusive 64. True or False: If P(A or B) = 1.0, then A and B must be mutually exclusive. ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: mutually exclusive, collective exhaustive 65. True or False: If P(A or B) = 1.0, then A and B must be collectively exhaustive. ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: collective exhaustive Basic Probability 105 66. True or False: If P(A and B) = 0, then A and B must be mutually exclusive. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: mutually exclusive 67. True or False: If P(A and B) = 0, then A and B must be collectively exhaustive. ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: collectively exhaustive, mutually exclusive 68. True or False: If P(A and B) = 1, then A and B must be collectively exhaustive. ANSWER: True TYPE: TF DIFFICULTY: Difficult KEYWORDS: collective exhaustive 69. True or False: If P(A and B) = 1, then A and B must be mutually exclusive. ANSWER: False TYPE: TF DIFFICULTY: Difficult KEYWORDS: mutually exclusive, collective exhaustive 70. Suppose A and B are independent events where P(A) = 0.4 and P(B) = 0.5. Then P(A and B) = __________. ANSWER: 0.2 TYPE: FI DIFFICULTY: Easy KEYWORDS: statistical independence, multiplication rule 71. Suppose A and B are mutually exclusive events where P(A) = 0.4 and P(B) = 0.5. Then P(A and B) = __________. ANSWER: 0 TYPE: FI DIFFICULTY: Easy KEYWORDS: mutually exclusive, joint probability, multiplication rule 106 Basic Probability 72. Suppose A and B are mutually exclusive events where P(A) = 0.4 and P(B) = 0.5. Then P(A or B) = __________. ANSWER: 0.9 TYPE: FI DIFFICULTY: Easy KEYWORDS: mutually exclusive, addition rule 73. Suppose A and B are independent events where P(A) = 0.4 and P(B) = 0.5. Then P(A or B) = __________. ANSWER: 0.7 TYPE: FI DIFFICULTY: Easy KEYWORDS: statistical independence, addition rule 74. Suppose A and B are events where P(A) = 0.4, P(B) = 0.5, and P(A and B) = 0.1. Then P(A or B) = __________. ANSWER: 0.8 TYPE: FI DIFFICULTY: Easy KEYWORDS: addition rule 75. Suppose A and B are events where P(A) = 0.4, P(B) = 0.5, and P(A and B) = 0.1. Then P(A|B) = __________. ANSWER: 0.2 TYPE: FI DIFFICULTY: Moderate KEYWORDS: conditional probability 76. Suppose A and B are events where P(A) = 0.4, P(B) = 0.5, and P(A and B) = 0.1. Then P(B|A) = __________. ANSWER: 0.25 TYPE: FI DIFFICULTY: Moderate KEYWORDS: conditional probability Basic Probability 107 TABLE 4-3 A survey is taken among customers of a fast-food restaurant to determine preference for hamburger or chicken. Of 200 respondents selected, 75 were children and 125 were adults. 120 preferred hamburger and 80 preferred chicken. 55 of the children preferred hamburger. 77. Referring to Table 4-3, the probability that a randomly selected individual is an adult is __________. ANSWER: 125/200 TYPE: FI DIFFICULTY: Moderate KEYWORDS: empirical classical probability, conditional probability, marginal probability 78. Referring to Table 4-3, the probability that a randomly selected individual is an adult or a child is __________. ANSWER: 200/200 TYPE: FI DIFFICULTY: Moderate KEYWORDS: empirical classical probability, addition rule 79. Referring to Table 4-3, the probability that a randomly selected individual is a child and prefers chicken is __________. ANSWER: 20/200 TYPE: FI DIFFICULTY: Moderate KEYWORDS: empirical classical probability, joint probability, multiplication rule 80. Referring to Table 4-3, the probability that a randomly selected individual is an adult and prefers chicken is __________. ANSWER: 60/200 TYPE: FI DIFFICULTY: Moderate KEYWORDS: empirical classical probability, joint probability, multiplication rule 81. Referring to Table 4-3, the probability that a randomly selected individual is a child or prefers hamburger is __________. ANSWER: 140/200 TYPE: FI DIFFICULTY: Moderate KEYWORDS: empirical classical probability, addition rule 108 Basic Probability 82. Referring to Table 4-3, assume we know the person is a child. The probability that this individual prefers hamburger is __________. ANSWER: 55/75 TYPE: FI DIFFICULTY: Moderate KEYWORDS: empirical classical probability, conditional probability 83. Referring to Table 4-3, assume we know that a person has ordered chicken. The probability that this individual is an adult is __________. ANSWER: 60/80 TYPE: FI DIFFICULTY: Moderate KEYWORDS: empirical classical probability, conditional probability, Bayes' theorem 84. Referring to Table 4-3, assume we know that a person has ordered hamburger. The probability that this individual is a child is __________. ANSWER: 55/120 TYPE: FI DIFFICULTY: Moderate KEYWORDS: empirical classical probability, conditional probability, Bayes' theorem TABLE 4-4 Suppose that patrons of a restaurant were asked whether they preferred beer or whether they preferred wine. 70% said that they preferred beer. 60% of the patrons were male. 80% of the males preferred beer. 85. Referring to Table 4-4, the probability that a randomly selected patron prefers wine is __________. ANSWER: 0.30 TYPE: FI DIFFICULTY: Moderate KEYWORDS: addition rule, multiplication rule, marginal probability 86. Referring to Table 4-4, the probability that a randomly selected patron is a female is __________. ANSWER: 0.40 TYPE: FI DIFFICULTY: Moderate KEYWORDS: addition rule, multiplication rule, marginal probability Basic Probability 109 87. Referring to Table 4-4, the probability that a randomly selected patron is a female who prefers wine is __________. ANSWER: 0.18 TYPE: FI DIFFICULTY: Difficult KEYWORDS: addition rule, multiplication rule, joint probability 88. Referring to Table 4-4, the probability that a randomly selected patron is a female who prefers beer is __________. ANSWER: 0.22 TYPE: FI DIFFICULTY: Difficult KEYWORDS: addition rule, multiplication rule, joint probability 89. Referring to Table 4-4, suppose a randomly selected patron prefers wine. The probability that the patron is a male is __________. ANSWER: 0.40 TYPE: FI DIFFICULTY: Difficult KEYWORDS: addition rule, multiplication rule, conditional probability 90. Referring to Table 4-4, suppose a randomly selected patron prefers beer. The probability that the patron is a male is __________. ANSWER: 0.69 TYPE: FI DIFFICULTY: Difficult KEYWORDS: addition rule, multiplication rule, conditional probability 91. Referring to Table 4-4, suppose a randomly selected patron is a female. The probability that the patron prefers beer is __________. ANSWER: 0.55 TYPE: FI DIFFICULTY: Difficult KEYWORDS: addition rule, multiplication rule, conditional probability 92. True or False: Referring to Table 4-4, the two events "liking" beer and "liking" wine are statistically independent. ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: addition rule, multiplication rule, statistical independence 110 Basic Probability 93. True or False: Referring to Table 4-4, the two events "liking" beer and being a male are statistically independent. ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: addition rule, multiplication rule, statistical independence TABLE 4-5 In a meat packaging plant, Machine A accounts for 60% of the plant's output, while Machine B accounts for 40% of the plant's output. In total, 4% of the packages are improperly sealed. Also, 3% of the packages are from Machine A and are improperly sealed. 94. Referring to Table 4-5, if a package is selected at random, the probability that it will be properly sealed is ________. ANSWER: 0.96 TYPE: FI DIFFICULTY: Moderate KEYWORDS: addition rule, marginal probability 95. Referring to Table 4-5, if a package selected at random is improperly sealed, the probability that it came from Machine A is ________. ANSWER: 0.75 TYPE: FI DIFFICULTY: Difficult KEYWORDS: conditional probability 96. Referring to Table 4-5, if a package selected at random came from Machine A, the probability that it is improperly sealed is ________. ANSWER: 0.05 TYPE: FI DIFFICULTY: Difficult KEYWORDS: conditional probability 97. Referring to Table 4-5, if a package selected at random came from Machine B, the probability that it is properly sealed is ________. ANSWER: 0.975 TYPE: FI DIFFICULTY: Difficult KEYWORDS: conditional probability, complement, addition rule Basic Probability 111 98. Referring to Table 4-5, if a package selected at random came from Machine B, the probability that it is improperly sealed is ________. ANSWER: 0.025 TYPE: FI DIFFICULTY: Difficult KEYWORDS: conditional probability, complement, addition rule TABLE 4-6 At a Texas college, 60% of the students are from the southern part of the state, 30% are from the northern part of the state, and the remaining 10% are from out of state. All students must take and pass an Entry Level Math (ELM) test. 60% of the southerners have passed the ELM, 70% of the northerners have passed the ELM, and 90% of the out-of-staters have passed the ELM. 99. Referring to Table 4-6, the probability that a randomly selected student is someone from northern Texas who has not passed the ELM is ________. ANSWER: 0.09 TYPE: FI DIFFICULTY: Difficult KEYWORDS: joint probability, multiplication rule 100. Referring to Table 4-6, the probability that a randomly selected student has passed the ELM is ________. ANSWER: 0.66 TYPE: FI DIFFICULTY: Difficult KEYWORDS: marginal probability, multiplication rule, addition rule 101. Referring to Table 4-6, if a randomly selected student has passed the ELM, the probability that the student is from out of state is ________. ANSWER: 0.136 TYPE: FI DIFFICULTY: Difficult KEYWORDS: conditional probability, Bayes' theorem 102. Referring to Table 4-6, if a randomly selected student has not passed the ELM, the probability that the student is from southern Texas is ________. ANSWER: 0.706 TYPE: FI DIFFICULTY: Difficult KEYWORDS: conditional probability, complement, Bayes' theorem 112 Basic Probability 103. Referring to Table 4-6, the probability that a randomly selected student is not from southern Texas and has not passed the ELM is ________. ANSWER: 0.10 TYPE: FI DIFFICULTY: Difficult KEYWORDS: joint probability, complement, multiplication rule, addition 104. Referring to Table 4-6, if a randomly selected student has not passed the ELM, the probability that the student is not from northern Texas is ________. ANSWER: 0.735 TYPE: FI DIFFICULTY: Difficult KEYWORDS: conditional probability, complement, addition rule, multiplication rule, Bayes' theorem 105. Referring to Table 4-6, if a randomly selected student is not from southern Texas, the probability that the student has not passed the ELM is ________. ANSWER: 0.25 TYPE: FI DIFFICULTY: Difficult KEYWORDS: conditional probability, complement, addition rule, multiplication rule, Bayes' theorem 106. Referring to Table 4-6, if a randomly selected student is not from out of state, the probability that the student has passed the ELM is ________. ANSWER: 0.633 TYPE: FI DIFFICULTY: Difficult KEYWORDS: conditional probability, complement, addition rule, multiplication rule, Bayes' theorem Basic Probability 113 TABLE 4-7 The next state lottery will have the following payoffs possible with their associated probabilities. Payoff Probability $2.00 0.0500 $25.00 0.0100 $100.00 0.0050 $500.00 0.0010 $5,000.00 0.0005 $10,000.00 0.0001 You buy a single ticket. 107. Referring to Table 4-7, the probability that you win any money is ________. ANSWER: 0.0666 TYPE: FI DIFFICULTY: Easy KEYWORDS: addition rule 108. Referring to Table 4-7, the probability that you win at least $100.00 is ________. ANSWER: 0.0066 TYPE: FI DIFFICULTY: Easy KEYWORDS: addition rule 109. Referring to Table 4-7, if you have a winning ticket, the probability that you win at least $100.00 is ________. ANSWER: 0.1 TYPE: FI DIFFICULTY: Moderate KEYWORDS: conditional probability, addition rule 110. A new model car from Ford Motor Company offers a keyless entry system that utilizes a fourletter code. How many different possible combinations are there for the code? ANSWER: 456976 TYPE: PR DIFFICULTY: Easy KEYWORDS: counting rule 111.At the International Pancakes Hut, there are 4 different ways to have an egg cooked, 7 different choices of pancakes, 5 different types of syrups and 8 different beverages. How many different ways are there to order an egg, a pancake with a choice of syrup, and a beverage? ANSWER: 1120 TYPE: PR DIFFICULTY: Easy KEYWORDS: counting rule 114 Basic Probability 112. There are 10 finalists at a national dog show. How many different orders of finishing can there be for all the 10 finalists? ANSWER: 3628800 TYPE: PR DIFFICULTY: Easy KEYWORDS: counting rule, permutation 113. Eleven freshmen are to be assigned to eleven empty rooms in a student dormitory. Each room is considered unique, so that it matters who is being assigned to which room. How many different ways can those eleven freshmen be allocated? ANSWER: 39916800 TYPE: PR DIFFICULTY: Easy KEYWORDS: counting rule, permutation 114. There are only 4 empty rooms available in a student dormitory for eleven new freshmen. Each room is considered unique, so that it matters who is being assigned to which room. How many different ways can those 4 empty rooms be filled? ANSWER: 7920 TYPE: PR DIFFICULTY: Easy KEYWORDS: counting rule, permutation 115. There are only 4 empty rooms available in a student dormitory for eleven new freshmen. All the rooms are considered homogenous, so that it does not matter who is being assigned to which room. How many different ways can those 4 empty rooms be filled? ANSWER: 330 TYPE: PR DIFFICULTY: Easy KEYWORDS: counting rule, combination 116. Four freshmen are to be assigned to eleven empty rooms in a student dormitory. All the rooms are considered homogenous, so that it does not matter who is being assigned to which room. How many different ways can those 4 freshmen be assigned? ANSWER: 330 TYPE: PR DIFFICULTY: Easy KEYWORDS: counting rule, combination Basic Probability 115 117. There are 47 contestants at a national dog show. How many different top three finishes can there be? ANSWER: 97290 TYPE: PR DIFFICULTY: Easy KEYWORDS: counting rule, permutation 118. Seven passengers are on a waiting list for an overbooked flight. As a result of cancellations, 3 seats become available. How many different ways can those 3 available seats be filled, regardless of the order? ANSWER: 35 TYPE: PR DIFFICULTY: Easy KEYWORDS: counting rule, combination 119. A high school debate team of 4 is to be chosen from a class of 35. How many possible ways can the team be formed? ANSWER: 52360 TYPE: PR DIFFICULTY: Easy KEYWORDS: counting rule, combination 120. A debate team of 4 is to be chosen from a class of 35. There are two twin brothers in the class. How many possible ways can the team be formed which will include only one of the twin brothers? ANSWER: 10912 TYPE: PR DIFFICULTY: Moderate KEYWORDS: counting rule, combination 121. A debate team of 4 is to be chosen from a class of 35. There are two twin brothers in the class. How many possible ways can the team be formed which will not include either of the twin brothers? ANSWER: 40920 TYPE: PR DIFFICULTY: Moderate KEYWORDS: counting rule, combination 122. A debate team of 4 is to be chosen from a class of 35. There are two twin brothers in the class. How many possible ways can the team be formed which will include both of the twin brothers? ANSWER: 528 TYPE: PR DIFFICULTY: Moderate KEYWORDS: counting rule, combination 123. An exploration team of 2 women and 3 men is to be chosen from a candidate pool of 6 women and 7 men. How many different ways can this team of 5 be formed? 116 Basic Probability ANSWER: 525 TYPE: PR DIFFICULTY: Moderate KEYWORDS: counting rule, combination 124. Twelve students in a Business Statistics class are to be formed into three teams of four. How many different ways can this be done? ANSWER: 5775 TYPE: PR DIFFICULTY: Difficult EXPLANATION: 12!/ 4!8! 8!/ 4!4! / 3! KEYWORDS: counting rule, combination