Question

Three machines turn out all the products in a factory, with the first machine producing 15% of the products, the second machine 25%, and the third machine 60%. The first machine produces defective products 20% of the time, the second machine 3% of the time and the third machine 5% of the time. What is the probability that a non-defective product came from the second machine? (Round your answer to four decimal places.)

Answer 1

Machine	% production	Defective	Non defective
1st	0.15	0.20	0.80
2nd	0.25	0.03	0.97
3rd	0.60	0.05	0.95

P(second machine / non defective) = P(second machine and non defective) / P(non defective)

P(second machine and non defective)= 0.2425

P(non defective) = 0.15 * 0.80 + 0.25 * 0.97 + 0.60 * 0.95 = 0.9325

P(second machine / non defective) = = 0.2425 / 0.9325 = 0.2601

ANS: Probability that a non-defective product came from the second machine = 0.2601