Mensa is a high IQ society that admits people as members if they can score at the 98th percentile or above on certain standardized IQ (intelligence quotient) tests. On one such test, the Stanford Binet, the qualifying score is 132. The test consists of n questions, each with m choices.

On any given test question, the person taking the test knows the answer with probability p. Assume that when the person does not know the answer, the person guesses an option completely at random. Calculate the probability a person knew the answer to a question, given that they answered it correctly.