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An automobile plant contracted to buy shock absorbers from two suppliers X and Y. X supplies 60% 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
- 0.288
- 0.334
- 0.667
- 0.720
Correct answer: 0.334
Solution
This is a Bayes' theorem problem. The probability of reliability is $0.6\times0.96 + 0.4\times0.72 = 0.864$, and the probability that a reliable shock absorber came from Y is $(0.4\times0.72)/0.864 = 0.3333\approx 0.334$.
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