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NDA 2026 · PYQ · Probability / Bayes' Theorem · medium

In an entrance test there are multiple choice questions. There are four options for each question, of which only one is correct. The probability that a student knows the answer to a question is 90%. If he gets the correct answer to a question, then what is the probability that he was guessing?

Answer

The correct answer is C: 1/37. Let K = student knows, G = student guesses, C = correct answer. P(K) = 0.9, P(G) = 0.1.

  1. A.37/40
  2. B.36/37
  3. C.1/37✓ Correct
  4. D.1/40

Explanation

Let K = student knows, G = student guesses, C = correct answer. P(K) = 0.9, P(G) = 0.1. P(C|K) = 1, P(C|G) = 1/4. By Bayes' theorem, P(G|C) = P(G)P(C|G) / [P(K)P(C|K) + P(G)P(C|G)] = (0.1)(1/4) / [(0.9)(1) + (0.1)(1/4)] = (1/40) / (9/10 + 1/40) = (1/40) / (36/40 + 1/40) = (1/40) / (37/40) = 1/37.
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