A committee of 7 politicians is chosen from 10 liberal members, 8 democratic members and 5 independents.
(a)In how many ways can this be done so as to include exactly 1 independent and at least 3 liberal members and at least 1 democratic member?
A survey is conducted to study customer behavior at a convenience store. It is found that 70% of the customers patronize the convenience store everyday, 56% of the customers purchase newspapers from the convenience store. For those customers who patronize the convenience store everyday, 75% of them purchase newspapers from the convenience store.
(b)Calculate the probability that a randomly selected customer patronizes the convenience store everyday and purchases newspapers from the convenience store.
(c)Given that a customer purchases newspapers from the convenience store, what is the probability that thiscustomer patronizes the convenience store everyday?
(d)Given that a customer does not patronize the convenience store everyday, what is theprobability that this customer purchases newspapers from the convenience store?
Maths
2010-11-03 9:56 am
回答 (1)
2010-11-03 7:24 pm
✔ 最佳答案
(a). For 7 politicians, it can be one I , at least 3 L and at least 1 D, so the remaining 2 can be 2L, 2D or 1L 1D, so the combination are :1) 1 I , 5 L , 1 D
2) 1 I, 3 L, 3 D.
3) 1 I, 4 l, 2 D.
For case(1), it is 1 out of 5 I, 5 out of 10 L and 1 out of 8 D, so combination = (5C1)(10C5)(8C1) = 10080
For case(2), combination = (5C1)(10C3)(8C3) = 33600
For case(3), combination = (5C1)(10C4)(8C2) = 29400
So total combination = 10080 + 33600 + 29400 = 73080.
(b)
P(Patronized customers) = 0.7
P(Purchase newspaper) = 0.56
P(Purchase newspaper|patronized customers) = 0.75
By Law of Conditional Probability, P(Purchase newspaper and patronized customers) = P(Purchase newspaper|patronized customers)P(Patronized customers) = 0.75 x 0.7 = 0.525.
(c) Again by Law of Conditional Probability, P(Patronized customers|purchase newspaper) = P(Patronized customers and purchase newspaper)/P(Purchase newspaper) = 0.525/0.56 = 0.9375
(d) By Law of Total Probability,P(Purchase newspaper) = P(Purchase newspaper|patronized customers)P(Patronized customers) + P(Purchase newspaper|Not patronized customers)P(Not patronized customers)
so 0.56 = 0.75 x 0.7 + P(Purchase newspaper|Not patronized customers) x ( 1 - 0.7)
0.56 = 0.525 + 0.3 x P(Purchase newspaper|Not patronized customers)
so P(Purchase newspaper|Not patronized customers) = (0.56 - 0.525)/0.3 = 0.1167.
收錄日期: 2021-04-13 17:36:57
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