Homework Set #6: Chapter 4: Exercises 34, 36, 38, 40, 44, 68, 74, 80, 82, 84
34.
0.3636, found by:
36.
0.8571, found by:
38. a. P(rural|c) = 0.10
b. P(c)P(rural|c) = (0.10)(0.10) = 0.01
c.
39. a. 78,960,960
b. 840, found by (7)(6)(5)(4). That is 7!/3!
c. 10, found by 5!/3!2!
40. a. 6,840
b. 504
c. 21
44.
3003, found by
48. Empirical
50. No, probability would be 0.00
52. a. 0.10, found by 50/500
b. Yes, mutually exclusive, because at the same time an envelope cannot contain, for example, a total offering of $2 and a total offering of $56.
c. 1.00
d. 0.60, found by 300/500
e. 0.90, found by 450/500 or 1 (50/500)
54. a. 4/52, or 0.077
b. 3/51, or 0.059
c. 0.0045, found by (4/52)(3/51)
56. a. Venn diagram
b. Complement rule
c. 1
58. a. 0.0440 found by (0.353)3
b. 0.2708 found by (1 0.353)3
60. 0.3059, found by (50/90)(49/89)
62. a. 0.40, found by 200/500
b. 0.60, found by 100/500 + 200/500
c. 0.60, found by (200/500) + (200/500) (100/500), General rule of addition
d. 0.33, found by 100/300
e. 0.1595, found by (200/500)(199/499)
64. a. 0.42
b. 0.70(0.40) = 0.28
c. 0.88
66. a. 0.625, found by 250/400
b. 0.250, found by 100/400
c. Smokes Male Female Total
Yes 75 25 100
No 175 125 300
Total 250 150 400
0.1875, found by 75/400
d. 0.6875, found by 250/400 + 100/400 75/400
68. a. (10)(9)(8) = 720
b. 0.00139, found by 1/720
c. 0.99583, found by 1 3/720
70. 4320 different meals, found by 4 x 3 x 12 x 6 x 5
4104 different early bird meals, found by (12 x 4 x 3 x 6) + (12 x 4 x 3 x 5) + (12 x 4 x 6 x 5) + (12 x 3 x 6 x 5)
72. 15, found by 5 x 3
74. 17,576,000 found by (26)(26)(26)(10)(10)(10)
76. a. 0.333, found by (6/10)(5/9)
b. 0.9286, found by 1 [(6/10)(5/9)(4/8)(3/7)]
c. dependent
78. a. The overall percent defective is 5.175,
found by (0.20)(0.03) + (0.30)(0.04) + (0.25)(0.07) + (0.25)(0.065)
b.
Using Bayes Rule:
c. Supplier Joint Revised
Tyson 0.00600 0.1159
Fuji 0.01200 0.2319
Kirkpatricks 0.01750 0.3382
Parts 0.01625 0.3140
Total 0.05175 1.0000
80. 0.99, found by 1 [((0.90)(0.90) + (0.90)(0.10) + (0.10)(0.90)]
82. The following tree diagram lists the probabilities
P(G) = Probability of guilty = 0.05
P(NG) = Probability of not guilty = 0.95
P(C|G) = Probability of correct assessment if guilty = 0.90
P(C|NG) = Probability of correct assessment if not guilty = 0.90
a. George will fire all those that fail the lie detector test, whether they are guilty or not.
P(fire) = (0.05)(0.90) + (0.95)(0.10) = 0.14
b.
P(G|F) =
c.
P(G|N) =
d. Georges policy is not very effective. About 2/3 of the time innocent people are fired. (The complement of part b)
84.
a.
P(G|A) =
b.
P(M|A) =
c.
P(P|A) =
