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CA Foundation · Quantitative Aptitude · Probability

A Surat textile trader buys cloth from two mills: Mill X supplies 70% of the stock and Mill Y supplies 30%. The probability of a piece being faulty is 0.04 for Mill X and 0.10 for Mill Y. A piece picked at random is found faulty. What is the probability that it came from Mill Y?

The probability is 30/58. Faulty pieces from X have probability 0.028 and from Y 0.030, totalling 0.058. Dividing Y's share 0.030 by 0.058 gives 30/58, which is about 0.517, higher than Y's prior of 0.3.

  1. A30/58Correct
  2. B28/58
  3. C3/10
  4. D30/100

Explanation

P(X and faulty) = 0.7 x 0.04 = 0.028. P(Y and faulty) = 0.3 x 0.10 = 0.030. Total faulty = 0.058. P(Y | faulty) = 0.030/0.058 = 30/58. Option 28/58 is the probability for Mill X, and 3/10 is the prior, ignoring the evidence.

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