GATE AG 2008 • Q24 MCQ • 2 Marks

Section 1: Engineering Mathematics

Probability and Statistics

Subtopic: Random variables

Question Statement:

In a factory 30% of the machines are assembled by robots and 70% are assembled by manual labour. Reliability of the first type of machines is 0.9 and that of the second type of machines is 0.8. One piece of machine was found to be reliable. The probability of the machine having been assembled by robot is

Options:

  • (A) 0.325
  • (B) 0.565
  • (C) 0.675
  • (D) 0.835

Official Answer Key:

A

Step-by-Step Solution & Explanation

Bayes' theorem: P(Robot|Reliable) = P(Robot)·P(Reliable|Robot) / [P(Robot)·P(Reliable|Robot) + P(Manual)·P(Reliable|Manual)] = (0.3×0.9)/[(0.3×0.9)+(0.7×0.8)] = 0.27/(0.27+0.56) = 0.27/0.83 = 0.325.

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