NDA 2026 · PYQ · Probability / Bayes' Theorem · medium
In an entrance examination there are multiple-choice questions. There are four choices for each question, out of which only one is correct. A student knows the answer of a question with probability 90%. If he gives the correct answer to a question, what is the probability that he was guessing?
A.37/40
B.36/37
C.1/37✓ Correct
D.1/40
Explanation
Let K = knows, G = guesses, C = correct. P(K) = 0.9, P(G) = 0.1, P(C|K) = 1, P(C|G) = 1/4. By Bayes' theorem: P(G|C) = P(C|G)P(G)/[P(C|K)P(K) + P(C|G)P(G)] = (0.1·0.25)/(0.9·1 + 0.1·0.25) = 0.025/0.925 = 25/925 = 1/37.
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