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 A, P (A|D), is closest to ________
A)0.700
B)0.824
C)0.176
D)0.300
E)0.698

Question

Quizplus · Accepted Answer

Let D be the event that a component is defective and A be the event that it is produced at plant A.
We want to find P(A|D)
Using Bayes theorem, 
P(A|D) = P(D|A) * P(A) / P(D)

We know P(A) = 0.7, P(D|A) = 0.02 and P(D|B) = 0.01.
Also P(D) = P(D|A) * P(A) + P(D|B) * P(B)
= 0.02 * 0.7 + 0.01 * 0.3
= 0.016

Substituting these values we get, 
P(A|D) = (0.02 * 0.7) / 0.016
= 0.824

Therefore, the revised probability that the component is produced at plant A given that it is defective is closest to 0.824, which is option B.

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