A60 ODD ANSWERS 29. If events A, B, and C are not mutually exclusive, then P1A and B and C2 must be added because P1A2 + P1B2 + P1C2 counts the intersection of all three events three times and -P1A and B2 - P1A and C2 - P1B and C2 subtracts the intersection of all three events three times. So, if P1A and B and C2 is not added at the end, then it will not be counted. Section 3.3 Activity (page 166) 1. Answers will vary. 2. The theoretical probability is 0.5, so the green line should be placed there. Section 3.4 (page 174) 1. The number of ordered arrangements of n objects taken r at a time Sample answer: An example of a permutation is the number of seating arrangements of you and three of your friends. 3. False. A permutation is an ordered arrangement of objects. 5. True 7. 15,120 9. 56 11. 0.076 13. 0.462 15. Permutation. The order of the 16 floats in line matters. 17. Combination. The order does not matter because the position of one captain is the same as the other. 19. 5040 21. 720 23. 357,840 25. 39,070,080 27. 2,042,040 29. 50,400 31. 184,756 33. 9880 35. 3640 37. 86,296,950 39. 0.024 41. 0.008 43. (a) 0.016 (b) 0.385 45. 0.001 47. 0.210 or 0.213 49. 0.0000015 51. 0.166 53. 0.070 55. 0.933 57. 0.086 59. 0.066 61. 0.001 Uses and Abuses for Chapter 3 (page 178) 1. 0.000001 2. 0.001 3. 0.001 Review Exercises for Chapter 3 (page 180) 1. H T T H H T H T H T T H T H T H H T T H H T H T T H T H T H 5HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT6; 4 3. 5January, February, March, April, May, June, July, August, September, October, November, December6; 3 5. 84 7. Empirical probability because prior counts were used to calculate the frequency of a part being defective 9. Subjective probability because it is based on opinion 11. Classical probability because all of the outcomes in the event and the sample space can be counted 13. 0.215 15. 1.25 * 10-7 17. 0.315 19. Independent. The outcomes of the first four coin tosses do not affect the outcome of the fifth coin toss. 21. Dependent.The outcome of taking a driver’s education course affects the outcome of passing the driver’s license exam. 23. 0.025. Yes, the event is unusual because its probability is less than or equal to 0.05. 25. Mutually exclusive. A jelly bean cannot be both completely red and completely yellow. 27. 0.9 29. 0.538 31. 0.583 33. 0.579 35. 0.180 37. 0.722 39. No. You do not know whether events A and B are mutually exclusive. 41. 110 43. 35 45. 2730 47. 2380 49. 0.000009 51. (a) 0.955 (b) 0.0000008 (c) 0.045 (d) 0.9999992 53. (a) 0.071 (b) 0.005 (c) 0.429 (d) 0.114 Quiz for Chapter 3 (page 184) 1. 450,000 2. (a) 0.700 (b) 0.650 (c) 0.774 (d) 0.948 (e) 0.038 (f) 0.587 (g) 0.310 (h) 0.557 3. The event in part (e) is unusual because its probability is less than or equal to 0.05. 4. Not mutually exclusive. A bowler can have the highest game in a 40-game tournament and still lose the tournament. Dependent. One event can affect the occurrence of the second event. 5. 2,193,360 6. (a) 2,481,115 (b) 1 (c) 2,572,999 7. (a) 0.964 (b) 0.0000004 (c) 0.9999996 Real Statistics—Real Decisions for Chapter 3 (page 186) 1. (a) Sample answer: Investigate the number of possible passwords when different sets of characters, such as lowercase and capital letters, numbers, and special characters, are used. (b) You could use the definition of theoretical probability, the Fundamental Counting Principle, and the Multiplication Rule. 2. (a) Sample answer: Allow lowercase letters, uppercase letters, and numerical digits. (b) Sample answer: Because there are 26 lowercase letters, 26 uppercase letters, and 10 numerical digits, there are 26 + 26 + 10 = 62 choices for each digit. So, there are 628 8-digit passwords and the probability of guessing a password correctly on one try is 1 628 , which is less than 1 608 .
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