A factory production line is manufacturing bolts using three machines, A, B and

Question

A factory production line is manufacturing bolts using three machines, A, B and C. Of the total output, machine A is responsible for 25%, machine B for 35% and machine C for the rest. It is known from previous experience with the machines that 5% of the output from machine A is defective, 4% from machine B and 2% from machine C. What is the probability that a randomly chosen bolt is defective? A bolt is chosen at random from the production line and found to be defective. What is the probability that it came from machine A?

Explanation / Answer

a) P(randomly chosen bolt is defective) = P(A) P(bolt defective / A) + P(B) P(bolt defective / B) +P(C) P(bolt defective / C) = 0.25*0.05 + 0.35*0.04 + 0.4*0.02 = 0.0345

B) P(A/ Bolt defective) = [P(A) * P(bolt defective/ A) ] / P(randomly chosen bolt is defective)

= 0.25*0.05 / 0.0345 = 0.0125/0.0345 = 0.3623

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