2018 Spring #8. An industrial plant purchases 60% of its electronic relays from

Question

2018 Spring #8. An industrial plant purchases 60% of its electronic relays from supplier 1, and the rest from supplier . Past records show that 5 percent of the relays from suppliers I are defective while 10 percent of those from supplier are defective. Suppose that a relay is chosen at random. (a) What is the probability that it is non-defective and came from supplier 1? (b) What is the probability that it is defective? (c) If the relay is defective what is the probability that it came from supplier II?

Explanation / Answer

P(supplier I) = 0.6

P(supplier II) = 0.4

P(defecrtive | supplier I) = 0.05

P(defective | supplier II) = 0.1

a) P(not defective | supplier 1) = 1 - P(defective | supplier I) = 1 - 0.05 = 0.95

P(not defective and supplier I) = P(not defective | supplier !) * P(supplier I) = 0.95 * 0.6 = 0.57

b) P(defective) = P(defecrtive | supplier I) * P(supplier I) + P(defecrtive | supplier II) * P(supplier II)

                        = 0.05 * 0.6 + 0.1 * 0.4

                        = 0.07

c) P(supplier II | defective) = P(defecrtive | supplier II) * P(supplier II) / P(defective)

                                           = 0.1 * 0.4 / 0.07

                                           = 0.5714

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