Solutions to Try Its
1.
| Outcome | Probability |
|---|---|
| Heads (H) | [latex]\frac{1}{2}[/latex] |
| Tails (T) | [latex]\frac{1}{2}[/latex] |
2. [latex]\frac{2}{3}[/latex]
3. [latex]\frac{7}{13}[/latex]
4. [latex]\frac{2}{13}[/latex]
5. [latex]\frac{5}{6}[/latex]
6. [latex]\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}[/latex]
Solutions to Odd-Numbered Exercises
1. probability; The probability of an event is restricted to values between [latex]0[/latex] and [latex]1[/latex], inclusive of [latex]0[/latex] and [latex]1[/latex].
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 [latex]A\text{ } \text{and }B[/latex] and a union of events [latex]A \text{and} B[/latex], the union includes either [latex]A \text{or} B[/latex] 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 [latex]0[/latex] and [latex]1[/latex].
7. [latex]\frac{1}{2}[/latex]
9. [latex]\frac{5}{8}[/latex]
11. [latex]\frac{1}{2}[/latex]
13. [latex]\frac{3}{8}[/latex]
15. [latex]\frac{1}{4}[/latex]
17. [latex]\frac{3}{4}[/latex]
19. [latex]\frac{3}{8}[/latex]
21. [latex]\frac{1}{8}[/latex]
23. [latex]\frac{15}{16}[/latex]
25. [latex]\frac{5}{8}[/latex]
27. [latex]\frac{1}{13}[/latex]
29. [latex]\frac{1}{26}[/latex]
31. [latex]\frac{12}{13}[/latex]
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. [latex]\frac{5}{12}[/latex]
37. [latex]0[/latex]
39. [latex]\frac{4}{9}[/latex]
41. [latex]\frac{1}{4}[/latex]
43. [latex]\frac{3}{4}[/latex]
45. [latex]\frac{21}{26}[/latex]
47. [latex]\frac{C\left(12,5\right)}{C\left(48,5\right)}=\frac{1}{2162}[/latex]
49. [latex]\frac{C\left(12,3\right)C\left(36,2\right)}{C\left(48,5\right)}=\frac{175}{2162}[/latex]
51. [latex]\frac{C\left(20,3\right)C\left(60,17\right)}{C\left(80,20\right)}\approx 12.49%[/latex]
53. [latex]\frac{C\left(20,5\right)C\left(60,15\right)}{C\left(80,20\right)}\approx 23.33%[/latex]
55. [latex]20.50+23.33 - 12.49=31.34%[/latex]
57. [latex]\frac{C\left(40000000,1\right)C\left(277000000,4\right)}{C\left(317000000,5\right)}=36.78%[/latex]
59. [latex]\frac{C\left(40000000,4\right)C\left(277000000,1\right)}{C\left(317000000,5\right)}=0.11%[/latex]