## Solutions to Try Its

1.

Outcome Probability
Heads (H) $\frac{1}{2}$
Tails (T) $\frac{1}{2}$

2. $\frac{2}{3}$

3. $\frac{7}{13}$

4. $\frac{2}{13}$

5. $\frac{5}{6}$

6. $\begin{array}{lll}\text{a}\text{. }\frac{1}{91};\hfill & \text{b}\text{. }\frac{\text{5}}{\text{91}};\hfill & \text{c}\text{. }\frac{86}{91}\hfill \end{array}$

## Solutions to Odd-Numbered Exercises

1. probability; The probability of an event is restricted to values between $0$ and $1$, inclusive of $0$ and $1$.

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 $A\text{ } \text{and }B$ and a union of events $A \text{and} B$, the union includes either $A \text{or} B$ 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 $0$ and $1$.

7. $\frac{1}{2}$

9. $\frac{5}{8}$

11. $\frac{1}{2}$

13. $\frac{3}{8}$

15. $\frac{1}{4}$

17. $\frac{3}{4}$

19. $\frac{3}{8}$

21. $\frac{1}{8}$

23. $\frac{15}{16}$

25. $\frac{5}{8}$

27. $\frac{1}{13}$

29. $\frac{1}{26}$

31. $\frac{12}{13}$

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. $\frac{5}{12}$

37. $0$

39. $\frac{4}{9}$

41. $\frac{1}{4}$

43. $\frac{3}{4}$

45. $\frac{21}{26}$

47. $\frac{C\left(12,5\right)}{C\left(48,5\right)}=\frac{1}{2162}$

49. $\frac{C\left(12,3\right)C\left(36,2\right)}{C\left(48,5\right)}=\frac{175}{2162}$

51. $\frac{C\left(20,3\right)C\left(60,17\right)}{C\left(80,20\right)}\approx 12.49%$

53. $\frac{C\left(20,5\right)C\left(60,15\right)}{C\left(80,20\right)}\approx 23.33%$

55. $20.50+23.33 - 12.49=31.34%$

57. $\frac{C\left(40000000,1\right)C\left(277000000,4\right)}{C\left(317000000,5\right)}=36.78%$

59. $\frac{C\left(40000000,4\right)C\left(277000000,1\right)}{C\left(317000000,5\right)}=0.11%$