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Machines A and B produce 60% and 40% of the items in a factory, with defect rates of 2% and 5% respectively. An item chosen at random is fo…

1352Medium DSSSB TGT Computer Science 0 replies 1 views
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Machines A and B produce 60% and 40% of the items in a factory, with defect rates of 2% and 5% respectively. An item chosen at random is found defective. The probability that it was produced by B is

  • A3/8
  • B2/5
  • C5/8
  • D1/2
Correct answer: C

Explanation

By Bayes' theorem, P(B | defective) = (0.4 × 0.05)/(0.6 × 0.02 + 0.4 × 0.05) = 0.020/0.032 = 5/8.
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