COMEDK 2025 Morning Solved Paper

Concept:This problem uses Bayes' theorem to find the conditional probability that the student was guessing, given that he answered correctly.Explanation:Let $K$ be the event that the student knows the answer, and $G$ be the event that he guesses.$P(K) = 0.9$ and $P(G) = 0.1$.If he knows the answer, he answers correctly with certainty: $P(C \mid K) = 1$.If he guesses, he picks one of four options randomly, so $P(C \mid G) = \frac{1}{4}$.We need $P(G \mid C)$, the probability that he was guessing given a correct answer.Using Bayes' theorem: $P(G \mid C) = \frac{P(C \mid G) P(G)}{P(C)}$.First, compute the total probability of a correct answer:$P(C) = P(K)P(C \mid K) + P(G)P(C \mid G) = 0.9 \times 1 + 0.1 \times \frac{1}{4} = 0.9 + 0.025 = 0.925$.Now, $P(G \mid C) = \frac{\frac{1}{4} \times 0.1}{0.925} = \frac{0.025}{0.925}$.Simplify: $\frac{0.025}{0.925} = \frac{25}{925} = \frac{1}{37}$.Answer:Option C: $\displaystyle \frac{1}{37}$.