A student answers a multiple choice examination with questions that have four possible answers each. Suppose that the probability that the student knows the answer to a question is 0.80 and the probability that the student guesses is 0.20. If the student guesses, the probability of guessing the correct answer is 0.25. The questions are independent, that is, knowing the answer on one question is not influenced by the other question.
(a) If there is one question on the exam and he answered the question correctly, what is the probability he knew the answer?
(b) If there are two questions on the exam and he answered both questions correctly, what is the probability he knew both answers?
(c) How would you generalize the above to n questions, that is, if the student answered an infinite number of questions correctly, what is the probability he knew the answers?
I know the answer to A using Bayes Theorem is
But I'm completely stuck on B and C.