Question

You have three suppliers (A,B,C) for a specific part and you purchase equal numbers from all three in random order. The parts are not marked for origin. Their defective rates 0.3, 0.2 and 0. 1% respectively. You are looking at a defective part. What is the probability that the part came from A? (

Answer 1

the probability that the part came from A given that the piece is defective is 1/2 (50%)

Explanation:

defining the event A= getting a defective piece , Bi=getting a piece from the i-th supplier and Ci= getting a defective piece from the i-th supplier=1/3 (since each supplier is equally likely to be chosen)

P(A)= ∑P(Bi)*P(Ci) = 1/3* 0.003 + 1/3* 0.002 + 1/3* 0.001 = 1/3 * 0.006 = 0.002

then from the theorem of Bayes

P(Ca/A)=P(Ca ∩ A) / P(A) = P(Ca)/P(A) = 1/3*0.003 / 0.002 = 1/2

P(Ca/A)= 1/2 (50%)

then the probability that the part came from A given that the piece is defective is 1/2 (50%)