Question
A student is a taking a multiple choice exam that has $n \geq 2$ choices. The student saw some of the answer key before the exam, so with probability $0 < p < 1$, they know the answer to a given question. If they know the answer, then they always get it correct. If they don't know the answer, the student guesses uniformly at random among the answer choices. Each question has exactly one correct answer. Given that a student got the answer correct, what is the probability that they knew the answer to the question? Answer this when $p = 2/3$ and $n = 6$.