A particular electronic component is produced at two plants for an electronics manufacturer.Plant A produces 70% of the components used and the remainder are produced by plant B.The probability that a component is defective is 0.02 if it is produced at plant A and 0.01 if it is produced at plant B.If the component is defective the revised probability it is produced at plant B, P (B|D), is closest to ________
A)0.3
B)0.01
C)0.003
D)0.176
E)0.017

Question

Quizplus · Accepted Answer

Let D be the event that a component is defective, and B be the event that a component is produced by Plant B.

We want to find P(B|D), the revised probability that the component is produced at plant B given that it is defective.

By Bayes' theorem, we have:

P(B|D) = P(D|B) * P(B) / P(D)

We know that P(D|B) = 0.01, P(D|A) = 0.02, P(B) = 0.3 (since 30% of components are produced by plant B), and:

P(D) = P(D|A) * P(A) + P(D|B) * P(B)
        = 0.02 * 0.7 + 0.01 * 0.3
        = 0.016

Therefore, we have:

P(B|D) = 0.01 * 0.3 / 0.016
        = 0.176

So the closest answer choice is D) 0.176.

A Particular Electronic Component Is Produced at Two Plants for an Electronics