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.)

P (A | D) = 0,25

Step-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 0,05

And finally the probability of defective part in the production is 10 % or 0,1 hence:

P (A | D) = [ (0,5) * 0,05 ] / 0,1

P (A | D) = 0,25