AN98 Answers: Chapter 13 13.2 Assess Your Understanding (page 923) 3. permutation 4. combination 5. ( ) − n n r ! ! 6. ( ) − n n r r ! ! ! 7. 30 9. 24 11. 1 13. 1680 15. 28 17. 35 19. 1 21. 10,400,600 23. {abc abd abe acb acd ace adb adc ade aeb aec aed bac bad bae bca bcd bce bda bdc bde bea bec bed cab cad cae cba cbd , , , , , , , , , , , , , , , , , , , , , , , , , , , , , cbe cda cdb cde cea ceb ced dab dac dae dba dbc dbe dca dcb dce dea deb dec eab eac ead eba ebc ebd eca ecb ecd , , , , , , , , , , , , , , , , , , , , , , , , , , , , } eda edb edc , , ; 60 25. { } 123, 124, 132, 134, 142, 143, 213, 214, 231, 234, 241, 243, 312, 314, 321, 324, 341, 342, 412, 413, 421, 423, 431, 432 ; 24 27. { } abc abd abe acd ace ade bcd bce bde cde , , , , , , , , , ; 10 29. { } 123, 124, 134, 234 ; 4 31. 16 33. 8 35. 24 37. 60 39. 18,278 41. 35 43. 1024 45. 120 47. 132,860 49. 336 51. 90,720 53. (a) 63 (b) 35 (c) 1 55. × 1.157 1076 57. 362,880 59. 660 61. 15 63. (a) 125,000; 117,600 (b) A better name for a combination lock would be a permutation lock because the order of the numbers matters. 68. 10 sq. ft 69. ( )( ) = − − g f x x x 4 2 2 2 70. ° = + ° = + ° = + sin75 2 6 4 ; cos15 1 2 2 3 or cos15 2 6 4 71. = a 80 5 72. + + + + + x x y x y x y xy y 10 40 80 80 32 5 4 3 2 2 3 4 5 73. ( ) = = − − x y 3, 1or 3, 1 74. ⎡ − ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ 6 6 14 5 75. i e 2 cos 5 6 sin 5 6 ; 2 i 5 /6 π π ( ) + π ⋅ 76. ( ) + + + + x x x 5 2 3 4 2 2 2 2 77. ( ) − − x x 16 30 3 2/5 Historical Problem (page 932) 1. (a) { } AAAA AAAB AABA AABB ABAA ABAB ABBA ABBB BAAA BAAB BABA BABB BBAA BBAB BBBA BBBB , , , , , , , , , , , , , , , (b) ( ) ( ) ( ) ( ) ( ) ( ) ( ) = + + = + + = = + = + = P A C C C P B C C wins 4, 2 4, 3 4, 4 2 6 4 1 16 11 16 ; wins 4, 3 4, 4 2 4 1 16 5 16 4 4 13.3 Assess Your Understanding (page 932) 1. equally likely 2. complement 3. F 4. T 5. 0, 0.01, 0.35, 1 7. Probability model 9. Not a probability model 11. (a) { } = S HH, HT, TH, TT (b) ( ) ( ) ( ) ( ) = = = = P P P P HH 1 4 , HT 1 4 , TH 1 4 , TT 1 4 13. (a) { } = S HH1, HH2, HH3, HH4, HH5, HH6, HT1, HT2, HT3, HT4, HT5, HT6, TH1, TH2, TH3, TH4, TH5, TH6, TT1, TT2, TT3, TT4, TT5, TT6 (b) Each outcome has the probability of 1 24 . 15. (a) { } = S HHH, HHT, HTH, HTT, THH, THT, TTH, TTT (b) Each outcome has the probability of 1 8 . 17. { } = S 1 Yellow, 1 Red, 1 Green, 2 Yellow, 2 Red, 2 Green, 3 Yellow, 3 Red, 3 Green, 4 Yellow, 4 Red, 4 Green ; each outcome has the probability of 1 12 ; thus, ( ) ( ) + = + = P P 2Red 4Red 1 12 1 12 1 6 . 19. { =S 1 Yellow Forward, 1 Yellow Backward, 1 Red Forward, 1 Red Backward, 1 Green Forward, 1 Green Backward, 2 Yellow Forward, 2 Yellow Backward, 2 Red Forward, 2 Red Backward, 2 Green Forward, 2 Green Backward, 3 Yellow Forward, 3 Yellow Backward, 3 Red Forward, 3 Red Backward, 3 Green Forward, 3 Green Backward, 4 Yellow Forward, 4 Yellow Backward, 4 Red Forward, 4 Red Backward, 4 Green Forward, } 4 Green Backward ; each outcome has the probability of 1 24 ; thus, ( ) ( ) + = + = P P 1 Red Backward 1 Green Backward 1 24 1 24 1 12 . 21. { =S 11 Red,11 Yellow,11 Green, 12 Red,12 Yellow, 12 Green,13 Red,13 Yellow, 13 Green, 14 Red, 14 Yellow, 14 Green, 21 Red, 21 Yellow, 21 Green, 22 Red, 22 Yellow, 22 Green, 23 Red, 23 Yellow, 23 Green, 24 Red, 24 Yellow, 24 Green, 31 Red, 31 Yellow, 31 Green, 32 Red, 32 Yellow, 32 Green, 33 Red, 33 Yellow, 33 Green, 34 Red, 34 Yellow, 34 Green, 41 Red, 41 Yellow, 41 Green, 42 Red, 42 Yellow, 42 Green, 43 Red, } 43 Yellow, 43 Green, 44 Red, 44 Yellow, 44 Green ; each outcome has the probability of 1 48 ; thus, { } = E 22 Red, 22 Green, 24 Red, 24 Green ; ( ) ( ) ( ) = = = P E n E n S 4 48 1 12 . 23. A, B, C, F 25. B 27. ( ) ( ) = = P H P T 4 5 ; 1 5 29. ( ) ( ) ( ) ( ) ( ) ( ) = = = = = = P P P P P P 1 3 5 2 9 ; 2 4 6 1 9 31. 3 10 33. 1 2 35. 1 6 37. 1 8 39. 1 4 41. 1 6 43. 1 18 45. 0.55 47. 0.70 49. 0.30 51. 0.926 53. 0.19 55. 0.21 57. 17 20 59. 11 20 61. 1 2 63. 19 50 65. 9 20 67. (a) 0.57 (b) 0.95 (c) 0.83 (d) 0.38 (e) 0.29 (f) 0.05 (g) 0.78 (h) 0.71 69. (a) 25 33 (b) 25 33 71. 0.167 73. ≈ 1 25,989,600 0.0000000385 75. 2; left; 3; down 76. ( ) −3, 3 3 77. { } 22 78. ( ) − − 2, 3, 1 79. −40 80. 10 3 81. 48 mph 82. 593 83. π + 8 12 square units 84. − + − + + x x x x 4 2 3 7 2 4 2 Review Exercises (page 936) 1. { } { } { } { } { } { } { } ∅, Dave , Joanne , Erica , Dave, Joanne , Dave, Erica , Joanne, Erica , Dave, Joanne, Erica 2. 17 3. 24 4. 29 5. 34 6. 7 7. 45 8. 25 9. 7 10. 336 11. 56 12. 60 13. 128 14. 3024 15. 1680 16. 91 17. 1,600,000 18. 216,000 19. 256 (allowing numbers with initial zeros, such as 011) 20. 12,600 21. (a) 381,024 (b) 1260 22. (a) × 8.634628387 1045 (b) 0.6531 (c) 0.3469 23. (a) 0.038 (b) 0.962 24. 4 9 25. 0.2; 0.26 26. (a) 0.68 (b) 0.58 (c) 0.32 Chapter Test (page 937) 1. 22 2. 3 3. 8 4. 45 5. 5040 6. 151,200 7. 462 8. There are 54,264 ways to choose 6 different colors from the 21 available colors. 9. There are 840 distinct arrangements of the letters in the word REDEEMED. 10. There are 56 different exacta bets for an 8-horse race. 11. There are 155,480,000 possible license plates using the new format. 12. (a) 0.95 (b) 0.30 13. (a) 0.25 (b) 0.55 14. 0.19 15. 0.000033069 16. ( ) = ≈ P exactly 2 fours 625 3888 0.1608
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