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Question

(B) Let $K$ be the event that the student knows the answer and $G$ be the event that the student guesses the answer.Let $C$ be the event that the stud

Vedclass · Accepted Answer

$\frac{1}{37}$

Vedclass · Answer

(B) Let $K$ be the event that the student knows the answer and $G$ be the event that the student guesses the answer.Let $C$ be the event that the student gets the correct answer.Given: $P(K) = 0.9$, $P(G) = 1 - 0.9 = 0.1$.If the student knows the answer, the probability of getting it correct is $P(C|K) = 1$.If the student guesses, the probability of getting it correct is $P(C|G) = \frac{1}{4} = 0.25$.Using Bayes' Theorem, the probability that the student was guessing given they got the answer correct is $P(G|C) = \frac{P(C|G)P(G)}{P(C|G)P(G) + P(C|K)P(K)}$.$P(G|C) = \frac{0.25 	imes 0.1}{(0.25 	imes 0.1) + (1 	imes 0.9)} = \frac{0.025}{0.025 + 0.9} = \frac{0.025}{0.925} = \frac{25}{925} = \frac{1}{37}$.

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