What is the probability that a student knows the answer given that he has answered it correctly,....? A large class in stochastic processes at at a school is taking a multiple choice test. For one particular question with m proposed multiple choice answers, the fraction of students who know the answer is p; the others will guess. The probability of answering the question correctly is 1 for the students who know the answer and 1/m for the ones who guess. What is the probability that a student knows the answer given that he has answered it correctly?

$p\left[p\left(1-n\right)+n\right]^{-1}$
Assuming that $n$ is the probably of getting the question correct for those who guess.  With reasonable assumption, $n=m^{-1}$.
