GATE AG 2013 • Q62 MCQ • 2 Marks

Section 8: General Aptitude

Quantitative Aptitude

Subtopic: Numerical Computation

Question Statement:

In a factory, two machines M1 and M2 manufacture 60% and 40% of the autocomponents respectively. Out of the total production, 2% of M1 and 3% of M2 are found to be defective. If a randomly drawn autocomponent from the combined lot is found defective, what is the probability that it was manufactured by M2?

Options:

  • (A) 0.35
  • (B) 0.45
  • (C) 0.5
  • (D) 0.4

Official Answer Key:

C

Step-by-Step Solution & Explanation

By Bayes' theorem: P(M2|defective) = P(M2)×P(def|M2) / [P(M1)×P(def|M1) + P(M2)×P(def|M2)] = (0.4×0.03) / (0.6×0.02 + 0.4×0.03) = 0.012/(0.012+0.012) = 0.012/0.024 = 0.5. Answer: (C).

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