A company produces 10 , 000 items per day. On a particular day 2500 items were produced on machine A , 3500 on machine B and 4000 on machine C . The probability that an item produced by the machines A , B , C to be defective is respectively 2 % , 3 % and 5 % . If one item is selected at random from the output and is found to be defective, then the probability that it was produced by machine C , is

Question

A company produces 10 , 000 items per day. On a particular day 2500 items were produced on machine A , 3500 on machine B and 4000 on machine C . The probability that an item produced by the machines A , B , C to be defective is respectively 2 % , 3 % and 5 % . If one item is selected at random from the output and is found to be defective, then the probability that it was produced by machine C , is, 10 71, 16 71, 40 71, 21 71

MARKS App · Accepted Answer

According to Baye's theorem: P C E = P E C · P C P E A P A + P E B P B + P E C P C Here, P A = 2500 10000 ; P B = 3500 10000 ; P C = 4000 10000 P E A = 2 100 ; P E B = 3 100 ; P E C = 5 100 ⇒ P C E = 5 100 4000 10000 2 100 2500 10000 + 3 100 3500 10000 + 5 100 4000 10000 = 2 × 20 71 ∴ P C E = 40 71

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