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.

Question

Mathematics

Arroyo

24 December, 23:59

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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Danny Mack · Answer 1

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