Project ForgeAn 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
- A0.288
- 0.334
- C0.667
- D0.720
Explanation
By Bayes' theorem: P(Y|Reliable) = P(Reliable|Y)P(Y) / [P(Reliable|Y)P(Y) + P(Reliable|X)P(X)] = (0.72*0.4) / (0.72*0.4 + 0.96*0.6) = 0.288 / (0.288 + 0.576) = 0.288 / 0.864 ≈ 0.334.
Source: GATE CS 2012 (2012)
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