A company manufacturing electronic components for home entertainment systems buys electrical connectors from three suppliers.It buys 23% of the connectors from supplier A,31% from supplier B,and 46% from supplier C.It finds that 1% of the connectors from supplier A are defective,2% of the connectors from supplier B are defective,and 3% 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)0.385
B)0.278
C)0.31
D)0.02
E)0.103

Question

Quizplus · Accepted Answer

We can use Bayes' theorem to find the probability that the defective connector came from supplier B:

P(B|D) = P(D|B) * P(B) / (P(D|A) * P(A) + P(D|B) * P(B) + P(D|C) * P(C))

where P(B|D) is the probability that the defective connector came from supplier B given that it is defective, P(D|B) is the probability that a connector from supplier B is defective (2%), P(B) is the probability that a connector comes from supplier B (31%), P(D|A) is the probability that a connector from supplier A is defective (1%), P(A) is the probability that a connector comes from supplier A (23%), P(D|C) is the probability that a connector from supplier C is defective (3%), and P(C) is the probability that a connector comes from supplier C (46%).

Plugging in the values, we get:

P(B|D) = (0.02 * 0.31) / (0.01 * 0.23 + 0.02 * 0.31 + 0.03 * 0.46) = 0.278

Therefore, the probability that the defective connector came from supplier B is 0.278 or approximately 0.28. Therefore, the best choice is B.

A Company Manufacturing Electronic Components for Home Entertainment Systems Buys