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標題:

Probability --

發問:

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?

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最佳解答:

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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