GATE 2012 CS (CS1) – Question 8

General Aptitude · Quantitative Aptitude: Data Interpretation, Arithmetic and Number Computation · 2 marks · Multiple choice

Supplier X provides 60% and Y 40% of a plant’s shock absorbers. A quality test identifies reliable units: 96% of X’s and 72% of Y’s pass. A randomly chosen absorber is reliable. What is the probability it came from Y?

0.288
0.334
0.667
0.720

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Show answer and explanation

Correct answer: (B) 0.334

Explanation

Bayes’s rule gives $P(Y|R)=0.4(0.72)/[0.6(0.96)+0.4(0.72)]=0.288/0.864=1/3$. The closest listed value is 0.334, B. The value 0.288 alone is the joint probability of Y and reliable.

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