An automobile plant contracted to buy shock absorbers from two suppliers X and Y. X supplies 60% of the shock absorbers and Y supplies 40% of the shock absorbers. All shock absorbers are subjected to a quality test. The ones that pass the quality test are considered reliable. Of X's shock absorbers, 96% are reliable. Of Y's shock absorbers, 72% are reliable. The probability that a randomly chosen shock absorber, which is found to be reliable, is made by Y is: A. 0.288 B. 0.334 C. 0.667 D. 0.720

GATE 2012 · General Aptitude · Conditional Probability · medium

Answer: P(Y | Reliable) = 0.334 (Option B)

1. Compute joint probabilities: P(R and X) = 0.96 * 0.60 = 0.576; P(R and Y) = 0.72 * 0.40 = 0.288
2. Compute total probability of being reliable: P(R) = 0.576 + 0.288 = 0.864
3. Apply Bayes' theorem: P(Y|R) = 0.288 / 0.864 = 1/3 = 0.3333... ≈ 0.334