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

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.