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 ________
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 the component is defective and B be the event that the component is produced at plant B. Then, we are asked to find P(B|D), the probability that the component is produced at plant B given that it is defective.

Using Bayes' theorem, we have:

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

We know that P(D|A) = 0.02 and P(D|B) = 0.01, so:

P(D) = P(D|A) * P(A) + P(D|B) * P(B)
     = 0.02 * 0.7 + 0.01 * 0.3
     = 0.015

Furthermore, P(B) = 1 - P(A) = 0.3. Therefore:

P(B|D) = P(D|B) * P(B) / P(D)
       = 0.01 * 0.3 / 0.015
       = 0.2

Therefore, the revised probability that the component is produced at plant B given that it is defective is 0.2 or 0.176 in decimal. The closest option is D.

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