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15.6: Chapter 7

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Jan 2, 2025
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- 15.5: Chapter 6
- 15.7: Chapter 8

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Your Turn

7.1

$4 \times 15 = 60$

7.2

$4 \times 15 \times 3 \times 2 = 360$

7.3

$3 \times 10 \times 10 \times 10 \times 10 \times 10 \times 26 \times 26 \times 26 = {\text{5,272,800,000}}$

7.4

1. 120

7.5

1. 720

2. 132

3. 70

7.6

1. 30

2. 24,024

3. 5,814

7.7

$_{15}{P_3} = 2{,}730$

7.8

1. combination

2. combination

7.9

1. 15

2. 45

3. 2,002

7.10

1. 30,856

2. 111,930

7.11

1. 290,004

7.12

$\{\heartsuit ,\spadesuit ,\clubsuit ,\diamondsuit\}$

2. {A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K}

3. {1, 2, 3, 4}

4. {3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

7.13

1. Independent

2. Dependent

7.14

1. {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}

7.15

1. {J

$\heartsuit$ Q

$\heartsuit$ , J

$\heartsuit$ K

$\heartsuit$ , Q

$\heartsuit$ J

$\heartsuit$ , Q

$\heartsuit$ K

$\heartsuit$ , K

$\heartsuit$ J

$\heartsuit$ , K

$\heartsuit$ Q

$\heartsuit$ }

7.16

$P(\text{H} < 5) = 1$

$0 < P(\text{H} < 4) < 1$

$P(\text{H} ≥ 5) = 0$

7.17

$\frac{1}{6}$

$\frac{2}{3}$

$\frac{1}{2}$

7.18

$\frac{5}16$

7.19

$\frac{1}{3}$

$\frac{1}{2}$

$\frac{2}{3}$

7.20

1. \(\frac13

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= 1.3\% \)

7.21

1. theoretical

2. subjective

3. empirical

7.22

$\frac1316$

7.23

$\frac14443680 = \frac{3}910$

7.24

1. \(1 - \frac

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\approx 10.7\%\)

2. \(\frac

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\approx 0.86\%\)

7.25

$13{:}3$

$12{:}4 = 3{:}1$

7.26

1. The odds for

$E$ are

$4{:}1$ and the odds against

$E$ are

$1{:}4$ .

7.27

$P(E) = \frac{1}16$

$P(E) = \frac2.53.5 \approx 0.714$

7.28

1. Mutually exclusive

2. Not mutually exclusive

3. Mutually exclusive

7.29

$\frac{4}10 + \frac{2}10 = \frac{3}{5}$

2. Not appropriate; the events are not mutually exclusive.

$\frac{3}10 + \frac{2}10 = \frac{1}{2}$

7.30

$\frac{1}{2}$

$\frac{2}{3}$

7.31

$\frac{1}{3}$

$1$

$\frac{2}{3}$

7.32

$\frac{3}28$

$\frac{3}56$

$\frac{3}28$

7.33

Roll	Probability
1	$\frac{1}{3}$
2	$\frac{1}{4}$
3	$\frac{1}{6}$
4	$\frac{1}12$
5	$\frac{1}12$
6	$\frac{1}12$

7.34

1. Not binomial (more than two outcomes)

2. Not binomial (not independent)

3. Binomial

4. Not binomial (number of trials isn’t fixed)

7.35

1. 0.146

2. 0.190

3. 0.060

7.36

1. 0.2972

2. 0.6615

3. 0.0919

4. 0.5207

5. 0.3643

7.37

$\frac10{3}$

$\frac{3}{2}$

$\frac25{4}$ = $6.25

7.38

1. If you roll the special die many times, the mean of the numbers showing will be around 3.33.

2. If you repeat the coin-flipping experiment many times, the mean of the number of heads you get will be around 1.5.

3. If you play this game many times, the mean of your winnings will be around $10.

7.39

1. If the player bets on 7, the expected value is

$- \$ 0.17$ .

2. If the player bets on 12, the expected value is

$- \$ 0.14$ .

3. If the player bets on any craps, the expected value is

$- \$ 0.11$ .
The best bet for the player is any craps; the best bet for the casino is the bet on 7.

Check Your Understanding

1. 540

2. 14

3. 1,024

4. 800

5. 25,920

6. 120

7. 120

8. 1,320

9. 1,680

10.

$_{15}{P_4} = 32{,}760$

11. permutations

12. combinations

13. 66

14. 560

15. 20

16. 560

17. {0, 1, 2, 3, 4, 5, 6}

18.

	Crinkle Fries	Curly Fries	Onion Rings
8 Nuggets	8 nuggets with crinkle fries	8 nuggets with curly fries	8 nuggets with onion rings
12 Nuggets	12 nuggets with crinkle fries	12 nuggets with curly fries	12 nuggets with onion rings

19. $A tree diagram with three stages. The tree diagram shows a node branching into three nodes labeled H, E, and S. The node, H branches into two nodes labeled A and B. Node, E leads to a node labeled C. Node, S branches into three nodes labeled J, K, and L. The possible outcomes are as follows: H A, H B, E C, S J, S K, and S L.$

20. {8 nuggets with crinkle fries, 8 nuggets with curly fries, 8 nuggets with onion rings, 12 nuggets with crinkle fries, 12 nuggets with curly fries, 12 nuggets with onion rings}

21. {history with Anderson, history with Burr, English with Carter, sociology with Johnson, sociology with Kirk, sociology with Lambert}

22.

$\frac{1}{4}$

23.

$\frac{1}{2}$

24.

$\frac{1}{2}$

25. 0

26. theoretically

27. subjectively

28. empirically

29.

${\text{number of heads}} > 20$

30. 89.9%

31. \(\frac

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\approx 0.278\%\)

32. \(\frac

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\approx 0.079\%\)

33. \(\frac

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\approx 0.16\%\)

34. \(\frac

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\approx 1.67\%\)

35. \(\frac

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\approx 1.9\%\)

36. \(\frac

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\approx 1.9\%\)

37.

$1{:}2$

38.

$5{:}1$

39.

$1{:}1$

40.

$3{:}5$

41.

$11{:}2$

42.

$\frac{4}13$

43.

$\frac{5}12$

44.

$\frac{3}{5}$

45.

$\frac{3}{5}$

46.

$\frac{3}{5}$

47.

$\frac{2}{5}$

48.

$\frac{2}{5}$

49.

$\frac{3}10$

50.

$\frac{1}{4}$

51.

$\frac{1}{9}$

52.

$\frac{1}{6}$

53.

$\frac{2}15$

54.

$\frac{4}45$

55.

$\frac{8}45$

56. No (more than two outcomes)

57. Yes

58. No (number of trials is not fixed)

59. 0.9453

60. 0.1366

61. 0.8230

62. 4.1

63. If you roll this die many times, the mean of the numbers rolled will be around 4.1.

64. $0.417

65. If you play this game many times, the mean of the amount won/lost each time will be about 42 cents.

66. Yes; the expected value is positive.

Your Turn

Check Your Understanding

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