11. A particular electronic component is produced at two plants for an electroni

Question

11. A particular electronic component is produced at two plants for an electronics manufacturer Plant A produces 60% of the components used and the remainder are produced by plant B. Among the components produced at plant A, the proportion of defective components is 1% Among the components produced at plant B, the proportion of defective compon If a compone at plant A is ents is 2% nt received by the manufacturer is defective, the probability that it was produced a) 0.1429 b) 0.2857 c) 0.4286 d) 0.5714 e) None of the above

Explanation / Answer

P(A)=0.6

P(B)=0.4

Also, P(Defective | A)= 0.01

and P(Defective | B)=0.02

Thus P(Defective)=P(Defective | A)*P(A)+ P(Defective | B)*P(B)=0.01*0.6+0.02*0.4=0.014

P(A|Defective)=P(Defective|A)*P(A)/P(Defective)=0.01*0.6/0.014=0.4286

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