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. Four percent of all the parts are defective. Three percent of the parts manufactured on machine A are defective. Find the probability that a part was manufactured on machine A, given that the part is defective. (Round your answer to 4 decimal places.)

Solution

Half of a set of parts are manufactured by machine A and half by machine B. Five percent of all parts are defective. P(d) = 0.05
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Two percent of the parts manufactured on machine A are defective.P(d|A)=0.02
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Find the probability that a part was manufactured on machine A, given that the part is defective

P(A|d) = P(A and d)/P(d) = [P(d|A)*P(A)]/P(d) = [0.02*0.5]/0.05
= 0.01/0.05 = 0.2 or 1/5