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. [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]