**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(A**_{1}) =\(\frac{9}{10}\) , P(A_{2}) = 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

**\(P(A_2/E) = \frac{P(A_2).P(E/A_2)}{P(A_1).P(E/A_1)+P(A_2).P(E/A_2)}\)**

= \(\frac{\frac{1}{10}.\frac{1}{4}}{\frac{9}{10}.1+\frac{1}{10}.\frac{1}{4}}\) = \(\frac{\frac{1}{40}}{\frac{37}{40}}\) = **\(\frac{1}{37}\)**