Question

A manufacturer has three machine operators A, B and C. The first operator A produces 1% defective items, where as the other two operators B and C produce 5% and 7% defective items respectively. A is on the job for 50% of the tune, B is on the job for 30% of the time and C is on the job for 20% of the time. A defective item is produced, what is the probability that it was produced by A? Select the correct answer from above options

Answer 1

`P(A) = 0.5` `P(B) = 0.3` `P(C) = 0.2` `P(D/A) = 0.01` `P(D/B) = 0.05` `P(D/C) = 0.07` By baes theorem `P(A/D) = (0.5 xx 0.01)/(0.5 xx 0.01 + 0.3 xx 0.05 + 0.2 xx 0.07) ` `= 5/(5 + 15 + 14) = 5/34` Answer