Suppose that in answering a multiple-choice test question with n choices, a student either knows the answer (with probability p), or the student guesses it.

Assume that the probability of answering a question correctly is 1 for a student who knows the answer. If the student guesses the answer, the student chooses one of the options with equal probability.

(a) In the case of a multiple-choice test question with 5 choices, what is the probability that the student knew the answer, given that the answer was correct?

(b) What is this probability in the case of a multiple-choice test question with 3 choices?

(c) What is this probability in the case of a true-false test question?