In a bulb factory, three machines, A, B, C, manufacture 60%, 25% and 15% of the total production respectively. Of their respective outputs, 1%, 2% and 1% are defective. A bulb is drawn at random from the total product, and it is found to be defective. Find the probability that it was manufactured by machine C.

Question

Philoid · Accepted Answer

Let

D : Bulb is defective

We want to find P(C|D), i.e. probability that the selected defective bulb is manufactured by C

Where, P(A) = probability that bulb is made by machine A

P(B) = probability that bulb is made by machine B

P(C) = probability that bulb is made by machine C

P(D|A) = probability of defective bulb from machine A

P(D|B) = probability of defective bulb from machine B

P(D|C) = probability of defective bulb from machine C

Conclusion: Therefore, the probability of selected defective bulb is from machine C is