ODD ANSWERS A59 33. 1. Simple event because it is an event that consists of a single outcome 35. 13. Not a simple event because it is an event that consists of more than a single outcome 37. 576 39. 4500 41. 0.083 43. 0.667 45. 0.333 47. 0.700 49. 0.092 51. 0.254 53. Empirical probability because company records were used to calculate the frequency of a car needing repairs 55. Subjective probability because it is most likely based on an educated guess 57. Classical probability because each outcome in the sample space is equally likely to occur 59. 0.457 61. 0.921 63. 0.648 65. (a) 0.001 (b) 0.999 67. 0.042; unusual 69. 0.208; not unusual 71. 0.125 73. 0.375 75. 0.033 77. 0.275 79. No. None of the events has a probability of 0.05 or less. 81. (a) 0.5 (b) 0.25 (c) 0.25 83. 0.091 85. 0.201 87. (a) 0.047 (b) 0.370 (c) 0.039. Both a and c are unusual because the probability is less than or equal to 0.05. 89. The probability of randomly choosing a smoker whose mother did not smoke 91. No. The odds of winning a prize are 1 : 6 (one winning cap and six losing caps). So, the statement should read, “one in seven game pieces wins a prize.” 93. (a) 0.444 (b) 0.556 95. 39 : 13 = 3 : 1 97. (a) Sum Probability 2 0.028 3 0.056 4 0.083 5 0.111 6 0.139 7 0.167 8 0.139 9 0.111 10 0.083 11 0.056 12 0.028 (b) Answers will vary. (c) Answers will vary. Section 3.1 Activity (page 146) 1 – 2. Answers will vary. Section 3.2 (page 152) 1. Two events are independent when the occurrence of one of the events does not affect the probability of the occurrence of the other event, whereas two events are dependent when the occurrence of one of the events does affect the probability of the occurrence of the other event. 3. The notation P1B0 A2 means the probability of event B occurring, given that event A has occurred. 5. False. If two events are independent, then P1A0 B2 = P1A2. 7. (a) 0.530 (b) 0.160 9. Independent. The outcome of the first draw does not affect the outcome of the second draw. 11. Dependent. The outcome of returning a movie after its due date affects the outcome of receiving a late fee. 13. Dependent. The sum of the rolls depends on which numbers came up on the first and second rolls. 15. Events: achievements in math and achievements in music; Dependent. There is a relationship between achievements in math and music. 17. Events: playing violent video games, aggressive or bullying behavior; Independent. Playing violent video games does not cause aggressive or bullying behavior in teens. 19. 0.063 21. 0.0016 23. (a) 0.563 (b) 0.063 (c) 0.938 25. (a) 0.032 (b) 0.672 (c) 0.328 (d) Both adults saying that Barack Obama was the best president in U.S. history is unusual because the probability is less than or equal to 0.05. 27. (a) 0.004 (b) 0.052 (c) 0.948 (d) The probability that all six people have type O+ blood is unusual because the probability is less than or equal to 0.05. 29. (a) 0.005 (b) 0.995 (c) Yes, this is unusual because the probability is less than or equal to 0.05. 31. 0.612 33. 0.444 35. 0.167 37. 0.792 39. (a) 0.074 (b) 0.999 41. 0.954 Section 3.3 (page 162) 1. P1A and B2 = 0 because A and B cannot occur at the same time. 3. True 5. False. The probability that event A or event B will occur is P1A or B2 = P1A2 + P1B2 - P1A and B2. 7. Not mutually exclusive. People can wear a polo shirt while wearing Bermuda shorts. 9. Not mutually exclusive. A freshman music major can be 20 years old. 11. Mutually exclusive. A voter cannot be both a Republican and a Democrat. 13. 0.625 15. 0.126 17. (a) 0.308 (b) 0.538 (c) 0.308 19. (a) 0.121 (b) 0.366 (c) 0.750 (d) 0.732 21. (a) 0.730 (b) 0.320 (c) 0.760 (d) 0.410 23. (a) 0.819 (b) 0.470 (c) 0.959 25. (a) 0.718 (b) 0.645 (c) 0.584 (d) 0.809 27. 0.63
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