Couplings are produced by a small manufacturer at three sites A, B.and C. 10% of
ID: 2916416 • Letter: C
Question
Couplings are produced by a small manufacturer at three sites A, B.and C. 10% of the couplings produced by site A are defective whereas5% of those produced by site B and 2% of those produced by site C are defective. Site Aproduces 50% of all couplings, site B produces 30% and site Cproduces 20%. Given that a coupling is defective, what is theprobability that it was produced by site A? 10% of the couplings produced by site A are defective whereas5% of those produced by site B and 2% of those produced by site C are defective. Site Aproduces 50% of all couplings, site B produces 30% and site Cproduces 20%. Given that a coupling is defective, what is theprobability that it was produced by site A?Explanation / Answer
Let E be the event that a coupling is defective. By law of totalprobability, P(E) = P(E|A)P(A)+P(E|B)P(B)+P(E|C)P(C) = 0.1 x 0.5 + 0.05 x 0.3 +0.02 x 0.2 = 0.05+0.015+0.004 = 0.069 Using Bayes Theorem, P(A|E) = {P(E|A)P(A)}/P(E) = 0.1 x 0.5 /0.069 = 0.7246