Half of a set of the parts are manufactured by machine A and half by machine B. Ten percent of all the parts are defective. Five 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.)

Answer:P ( A | D ) = 0,25Step-by-step explanation:The probability that a part was manufacture on machine A given that part is defective : P ( A | D )P ( A | D ) = [P (A) * P ( D | A )]/ P ( D )Where:   P (A ) is the probability that the part is manufacture in machine A which is 0,5 (half of the parts are manufacture in machine A) P ( D | A ) is the probability of defective part given that the part was manufacture in machine A which is 5% or 0,05And finally the probability of defective part in the production is 10 % or 0,1 hence :P ( A | D ) = [ ( 0,5 ) * 0,05 ] / 0,1P ( A | D ) = 0,25