A company producing electric relays has three manufacturing plants producing 33, 42, 25 percent, respectively, of its product. Assume that the probabilities that relay manufactured by such plants is defective are 0.04, 0.03, and 0.02, respectively.
a. If a relay is selected at random from this company, determine the probability that it is defective?
b. If a relay selected at random is found to be defective, determine the probability that it was manufactured by the second plant?