A company producing electric relays has four manufacturing plants producing 40,

Question

A company producing electric relays has four manufacturing plants producing 40, 30, 20 and 10 percent, respectively, of its product. Suppose the plants are independent and the probabilities that a relay manufactured by these plants is defective are 0.02,0. 05, 0.03 and 0.01, respectively. (a) If a relay is selected at random from the output of the company, what is the probability that is defective? If a relay selected at random is found to be defective, w hat is the probability that it is manufactured by plant 2 or plant 4?

Explanation / Answer

a)

Probability = 0.02 * 40 + 0.05 * 30 + 0.03 * 20 + 0.01*10= 3 / 80 = 0.0375

probability that is manufactured by plant 2 or 4 given that is defective = 0.05 * 0.01 / 0.0375 = 0.0133

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