A student takes a multiple-choice exam. Suppose for each question they either know the

answer or gamble and choose an option at random. Further suppose that if they knows the

answer, the probability of a correct answer is 1, and if they gamble, this probability is 1/4.

To pass, students need to answer at least 60% of the questions correctly. The student has

“studied for a minimal pass,” i.e., with probability 0.6 they know the answer to a question.

For a single question, given that they answers it correctly, what is the probability that they

actually knew the answer (Pick the closest answer)?