In answering a question on a multiple choice test, a student either knows the answer or he doesn't and he guesses. Let p be the probability that he knows the answer (1-p is therefore the probability that he guesses.) Assume that a student who guesses at the answer will be correct with probability 1/m, where m is the number of multiple choice alternatives.

What is the probability that a student knew the answer to a question given that he answered it correctly? Assume that if he knew the answer, he did not make a mistake and he wrote down the answer correctly, i.e. P (C|K) = 1.0.

P (K) = p        P (K') = 1 - p

a) Find P (K|C) in terms of m and p.

b) If there are 5 choices for a question and there is a 50% chance that the student knows the answer, what is the probability that the student knew the answer to a question he correctly answered?