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

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Solution

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Official answer: B) 0.334

Quantitative Aptitude

Let $X$ and $Y$ denote the events that a shock absorber is manufactured by supplier X and supplier Y, respectively. Let $R$ denote the event that a shock absorber is reliable.

From the given data:

$P(X) = 0.60$
$P(Y) = 0.40$
$P(R \mid X) = 0.96$
$P(R \mid Y) = 0.72$

Using Bayes' theorem, the probability that a reliable shock absorber was made by supplier Y is:

P(Y \mid R) = \frac{P(Y) \cdot P(R \mid Y)}{P(X) \cdot P(R \mid X) + P(Y) \cdot P(R \mid Y)}

Substitute the values:

P(Y \mid R) = \frac{0.40 \times 0.72}{(0.60 \times 0.96) + (0.40 \times 0.72)} = \frac{0.288}{0.576 + 0.288} = \frac{0.288}{0.864} = \frac{1}{3} \approx 0.334

Thus, the correct option is (B).

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This Quantitative Aptitude previous year question is Q63 of the GATE CSE 2012 paper. Find more GATE CSE PYQs on Quantitative Aptitude in General Aptitude, or browse all GATE CSE PYQs.

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Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.