A manufactu

Let E1 be the event that machine A is defective. P(E1) = 1%

Let E2 be the event that machine B is defective. P(E2) = 5%

Let E3 be the event that machine C is defective. P(E3) = 7%

Let A be the event that the item chosen is defective.

P(the defective item is manufactured by A) = P(A|E1) = 50%

P(the defective item is manufactured by B) = P(A|E2) = 30%

P(the defective item is manufactured by C) = P(A|E3) = 20%

Now, According to the Bayes’ theorem,

Given E1, E2, E3…….En are mutually exclusive and exhaustive events, we can find the conditional probability P(Ei|A) for any event A associated with Ei is given by:

Therefore,

The probability that defective item is produced by A,

Hence, the probability that the defective item is produced by machine A is .

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