simple probability

2013-02-06 12:04 pm

1. For 60 items, 4 are defective. If 4 items are drawn at random from the 60 items for inspection, what are the probabilities of drawing 3 defective items under the following conditions.

a) there is at least one defective item in the 4 items. answer = 0.0019
b) the first two inspected items are defective. answer = 0.0678

2. To promote customers' loyalty, ABC convenience store gives out free stickers to customers on each purchase. The store manager finds that only 45% of the customers are interested in stickers collection, where 20% of them are students. On average, 31% of the customers of the store are students. A customer is now chosen at random.

a) find the probability that the customer is a student, given that he/she is not interested in stickers collection. answer = 0.4
b) find the probability that the customer is neither interested in stickers collection nor a student. answer = 0.33

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回答 (1)

50418129

2013-02-06 5:16 pm

✔ 最佳答案

(1)(a)

P(3 defective among 4 items | at least 1 defective among 4 items)
= P(3 defective among 4 items and at least 1 defective among 4 items)
/ P(at least 1 defective among 4 items)
= P(3 defective among 4 items) / P(at least 1 defective among 4 items)
= [(4C3 x 56C1) / 60C4] / [1 - 56C4 / 60C4]
= 0.0019

(1)(b)

P(3 defective among 4 items | first 2 are defective among 4 items)
= P(3 defective among 4 items and first 2 are defective among 4 items)
/ P(first 2 are defective among 4 items)
= [(4/60)(3/59)(2/58)(56/57) + (4/60)(3/59)(56/58)(2/57)] / (4/60)(3/59)
= 0.0678

(2)(a)

P(the customer is a student) = 31%
P(the customer is a student and interested in collection) = 45% x 20%
P(the customer is a student and not interested in collection)
= 31% - 45% x 20%

P(the customer is a student | the customer is not interested in collection)
= P(the customer is a student and the customer is not interested in collection)
/ P(the customer is not interested in collection)
= (31% - 45% x 20%) / (1 - 45%)
= 0.4

(2)(b)

P(the customer is not a student) = 1 - 31%
P(the customer is not a student and interested in collection)= 45% x (1 - 20%)
P(the customer is not a student and not interested in collection)
= (1 - 31%) - 45% x (1 - 20%)
= 0.33

參考: knowledge

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