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23 November, 12:59

A computer manufacturer uses chips from three sources. Chips from sources A, B, and C are defective with probabilities 0.005, 0.001, and 0.010, respectively. You can assume that the proportions of chips from A, B and C are 0.5, 0.1, and 0.4 respectively. If a randomly selected chip is found to be defective, find the probability that the manufacturer was A and the probability that the manufacturer was C.

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  1. 23 November, 13:13
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    Step-by-step explanation:

    A="The chip is from the manufacturer A"

    B="The chip is from the manufacturer B"

    C="The chip is from the manufacturer C"

    D="The chip is defective"

    P (A) = 0.5

    P (B) = 0.1

    P (C) = 0.4

    P (D|A) = 0.005

    P (D|B) = 0.001

    P (D|C) = 0.01

    P (D) = P (D|A) P (A) + P (D|B) P (B) + P (D|C) P (C) = 0.005*0.5+0.001*0.1+0.01*0.4

    P (D) = 6.6x10-3

    Based on Bayes rule:

    P (A|D) = P (D|A) P (A) / P (D) = 0.005*0.5/6.6x10-3=0.38

    P (C|D) = P (D|C) P (C) / P (D) = 0.01*0.4/6.6x10-3=0.60
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