6. 115 pts, 5 each] A particular electronic component is produced at two plants

Question

6. 115 pts, 5 each] A particular electronic component is produced at two plants for an electronics manufacturer. Plant A produces 60% of the components used and the remainder is produced by plant B. The proportion of defective components produced at plant B is 190 and the proportion of defective components produced at plant A is 2% (a) What is the probability of receiving a defective component from these two plants? (b) If a component received by the manufacturer is defective, what is the probability that it was produced at plant A? (c) If a component received by the manufacturer is not defective, what is the probability that it was produced at plant A? Show all work.

Explanation / Answer

a)P(defective)=P(from plant A and defective+from plant B and defective) =0.6*0.02+(1-0.6)*0.01=0.016

b) P(plat A|defective) =P(from plant A and defective)/P(defective) =0.6*0.02/0.016=0.75

c)P(not defective) =1-P(defective =1-0.016 =0.984

hence P(plant A|not defective) =P(from plant A and not defective)/P(not defective) =0.6*(1-0.02)/0.984=0.597561

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