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Study Guides > Precalculus II

Solutions for Probability

Solutions to Try Its

1.
Outcome Probability
Roll of 1
Roll of 2
Roll of 3
Roll of 4
Roll of 5
Roll of 6
2. 23\frac{2}{3} 3. 713\frac{7}{13} 4. 213\frac{2}{13} 5. 56\frac{5}{6} 6. a. 191;b. 591;c. 8691\begin{array}{lll}\text{a}\text{. }\frac{1}{91};\hfill & \text{b}\text{. }\frac{\text{5}}{\text{91}};\hfill & \text{c}\text{. }\frac{86}{91}\hfill \end{array}

Solutions to Odd-Numbered Exercises

1. probability; The probability of an event is restricted to values between 00 and 11, inclusive of 00 and 11. 3. An experiment is an activity with an observable result. 5. The probability of the union of two events occurring is a number that describes the likelihood that at least one of the events from a probability model occurs. In both a union of sets A and BA\text{ } \text{and }B and a union of events AandBA \text{and} B, the union includes either AorBA \text{or} B or both. The difference is that a union of sets results in another set, while the union of events is a probability, so it is always a numerical value between 00 and 11. 7. 12\frac{1}{2}. 9. 58\frac{5}{8}. 11. 12\frac{1}{2}. 13. 38\frac{3}{8}. 15. 14\frac{1}{4}. 17. 34\frac{3}{4}. 19. 38\frac{3}{8}. 21. 18\frac{1}{8}. 23. 1516\frac{15}{16}. 25. 58\frac{5}{8}. 27. 113\frac{1}{13}. 29. 126\frac{1}{26}. 31. 1213\frac{12}{13}. 33.
1 2 3 4 5 6
1 (1, 1) 2 (1, 2) 3 (1, 3) 4 (1, 4) 5 (1, 5) 6 (1, 6) 7
2 (2, 1) 3 (2, 2) 4 (2, 3) 5 (2, 4) 6 (2, 5) 7 (2, 6) 8
3 (3, 1) 4 (3, 2) 5 (3, 3) 6 (3, 4) 7 (3, 5) 8 (3, 6) 9
4 (4, 1) 5 (4, 2) 6 (4, 3) 7 (4, 4) 8 (4, 5) 9 (4, 6) 10
5 (5, 1) 6 (5, 2) 7 (5, 3) 8 (5, 4) 9 (5, 5) 10 (5, 6) 11
6 (6, 1) 7 (6, 2) 8 (6, 3) 9 (6, 4) 10 (6, 5) 11 (6, 6) 12
35. 512\frac{5}{12}. 37. 00. 39. 49\frac{4}{9}. 41. 14\frac{1}{4}. 43. 34\frac{3}{4} 45. 2126\frac{21}{26} 47. C(12,5)C(48,5)=12162\frac{C\left(12,5\right)}{C\left(48,5\right)}=\frac{1}{2162} 49. C(12,3)C(36,2)C(48,5)=1752162\frac{C\left(12,3\right)C\left(36,2\right)}{C\left(48,5\right)}=\frac{175}{2162} 51. C(20,3)C(60,17)C(80,20)12.49\frac{C\left(20,3\right)C\left(60,17\right)}{C\left(80,20\right)}\approx 12.49% 53. C(20,5)C(60,15)C(80,20)23.33\frac{C\left(20,5\right)C\left(60,15\right)}{C\left(80,20\right)}\approx 23.33% 55. 20.50+23.3312.49=31.3420.50+23.33 - 12.49=31.34% 57. C(40000000,1)C(277000000,4)C(317000000,5)=36.78\frac{C\left(40000000,1\right)C\left(277000000,4\right)}{C\left(317000000,5\right)}=36.78% 59. C(40000000,4)C(277000000,1)C(317000000,5)=0.11\frac{C\left(40000000,4\right)C\left(277000000,1\right)}{C\left(317000000,5\right)}=0.11%

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