Answer: (b) \(\frac{1}{37}\)
We define the given events as:
A1: Student knows the answer
A2: Student does not know the answer
E: He gets the correct answer.
P(A1) =\(\frac{9}{10}\) , P(A2) = 1-\(\frac{9}{10}\) = \(\frac{1}{10}\)
\(\therefore\) P(E/A1) = P(Student gets the correct answer when he knows the answer) = 1
P(E/A2) = P(Student gets the correct answer when he does not know the correct answer) = 1/4
\(\therefore\) Required probability
\(P(A_2/E) = \frac{P(A_2).P(E/A_2)}{P(A_1).P(E/A_1)+P(A_2).P(E/A_2)}\)
= \(\frac{\frac{1}{10}.\frac{1}{4}}{\frac{9}{10}.1+\frac{1}{10}.\frac{1}{4}}\) = \(\frac{\frac{1}{40}}{\frac{37}{40}}\) = \(\frac{1}{37}\)