Use Bayes' theorem to find the indicated probability.
-A company manufacturing electronic components for home entertainment systems buys electrical connectors from three suppliers. It buys 24% of the connectors from supplier A, 36% from supplier B, and 40% from supplier C.
It finds that 2% of the connectors from supplier A are defective, 4% of the connectors from supplier B are defective, and 5% of the connectors from supplier C are defective.
If a customer buys one of these components and finds that the connector is defective, what is the probability that it came from supplier B?
A) 0.122
B) 0.04
C) 0.367
D) 0.581

Question

Quizplus · Accepted Answer

Using Bayes' theorem, the probability that a defective connector came from supplier B is calculated as follows: P(B|D) = [P(D|B) * P(B)] / P(D). P(D|B) = 0.04, P(B) = 0.36, and P(D) = (0.02*0.24) + (0.04*0.36) + (0.05*0.40) = 0.0384. Thus, P(B|D) = (0.04*0.36) / 0.0384 = 0.367.

Use Bayes' Theorem to Find the Indicated Probability