In answering a question on a multiple-choice test, a student either knows the answer or guesses. Let p be the probability that the student knows the answer and 1-p be the probability that the student guesses. Suppose there are 5 multiple-choice alternatives so a student who guesses at the answer will be correct with probability 1/5. (a) Show that the probability that a student knew the answer to a question given that he or she answered it correctly is 5p/(1+ 4p). (b) What is the probability that a student actually guessed the answer to a question given that he or she answered it correctly?

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