Allied & ICAR Exam Bank • ALLIED_1720 MCQ • 2 Marks

Section 8: General Aptitude

Quantitative Aptitude

Subtopic: Numerical Computation

Question Statement:

In a factory, machine X produces 60% of components with a 2% defect rate, and machine Y produces 40% with a 3% defect rate. If a randomly picked component is found to be defective, what is the probability it was made by machine X?

Options:

  • (A) 0.50
  • (B) 0.60
  • (C) 0.40
  • (D) 0.55

Answer Key:

A

Step-by-Step Solution & Explanation

$P(D) = 0.60(0.02) + 0.40(0.03) = 0.012 + 0.012 = 0.024$. By Bayes' theorem: $P(X|D) = 0.012 / 0.024 = 0.50$.
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