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Question

(C) 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

$\frac{5}{7}$

Vedclass · Answer

(C) 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 gives the correct answer.We are given:$P(C|G) = \frac{1}{2}$$P(C|K) = 1$ (since the student always gives the correct answer if he knows it).$P(G|C) = \frac{1}{6}$Let $P(K) = x$. Then $P(G) = 1 - x$.Using Bayes' theorem:$P(G|C) = \frac{P(C|G)P(G)}{P(C|G)P(G) + P(C|K)P(K)}$Substituting the values:$\frac{1}{6} = \frac{(\frac{1}{2})(1-x)}{(\frac{1}{2})(1-x) + (1)(x)}$$\frac{1}{6} = \frac{\frac{1-x}{2}}{\frac{1-x+2x}{2}}$$\frac{1}{6} = \frac{1-x}{1+x}$$1+x = 6-6x$$7x = 5$$x = \frac{5}{7}$Thus,the probability that the student knows the answer is $\frac{5}{7}$.

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