Probability --

tom insanity

2014-12-04 7:55 am

Buy iphone in lots of size 10
inspect 3 iphones randomly from a lot and to accept the lot only if all 3 are non-defective. If 30 percents of the lots have 4 defective i-phones and 70 percents have only 1 , what proportion of lots does the purchaser reject?

回答 (1)

知足常樂

2014-12-04 11:20 am

✔ 最佳答案

Pr(reject a lot)
= Pr(reject a lot | 4 def lot)Pr(4 def lot) + Pr(reject a lot | 1 def lot)Pr(1 def lot)
= Pr(reject a lot | 4 def lot)(30%) + Pr(reject a lot | 1 def lot)(70%)

Consider
Pr(reject a lot | 4 def lot)
= 1 - Pr(accept a lot | 4 def lot)
= 1 - (6/10)(5/9)(4/8)
= 5/6

Pr(reject a lot | 1 def lot)
= 1 - Pr(accept a lot | 1 def lot)
= 1 - (9/10)(8/9)(7/8)
= 3/10

Therefore,
Pr(reject a lot)
= Pr(reject a lot | 4 def lot)(30%) + Pr(reject a lot | 1 def lot)(70%)
= (5/6)(30%) + (3/10)(70%)
= 46%

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