A company producing electric relays has three manufacturing plants producing 50, 30, and

20 percent, respectively, of its product. Suppose that the probabilities that a relay

manufactured by these plants is defective are 0.02, 0.05, and 0.01, respectively.

a. If a relay is selected at random from the output of the company, what is the

probability that it is defective?

b. If a relay selected at random is found to be defective, what is the probability that it

was manufactured by plant 2?