In a factory, two machines M1 and M2 manufacture 70% and 30% of the autocomponents respectively. Out of the total production, 1% of M1 and 10% of M2 are found to be defective. If a randomly drawn autocomponent from the combined lot is found defective, what is the probability that it was manufactured by M2? A. 3/14 B. 7/13 C. 10/13 D. 14/13

GATE 2013 · General Aptitude · Conditional Probability · medium

Answer: P(M2 | defective) = 30/37 (answer key: C. 10/13)

1. Compute total probability of a defective component: P(D) = (0.01)(0.70) + (0.10)(0.30) = 0.007 + 0.030 = 0.037
2. Apply Bayes' theorem to find P(M2 | D): P(M2|D) = (0.10 * 0.30) / 0.037 = 0.030 / 0.037 = 30/37