Half of a set of the parts are manufactured by machine A and

Half of a set of the parts are manufactured by machine A and half by machine B. Nine percent of all the parts are deffective. Six percent of the parts manufactured on machine A are deffective. Find the probability that a part was manufactured on machine A. given that the part is deffective. (Round your answer to 4 decimal places.)

Solution

Let

A, B = they came from manufacturers A and B, respectively
D = defective

Thus,

P(A|D) = P(A n D) / P(D)

As

P(A n D) = P(A) P(D|A) = 0.50*0.06 = 0.03

P(D) = 0.09

Thus,

P(A|D) = 0.03/0.09 = 0.333333 [answer]