CASE STUDY

In answering a question on a multiple choice test for class XII, a student either knows the answer or guesses. Let $\frac{3}{5}$ be the probability that he knows the answer and $\frac{2}{5}$ be the probability that he guesses. Assume that a student who guesses at the answer will be correct with probability $\frac{1}{3}$. Let $E_1$, $E_2$, and E be the events that the student knows the answer, guesses the answer and answers correctly respectively. A student answers correctly if he/she knows the answer. Using the above information, answer the question: