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


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