A student takes a multiple choice test. Each question has N answers. If the student knows the answer to a question, the student gives the right answer, and otherwise guesses uniformly and at random. The student knows the answer to 70% of the questions. Write K for the event a student knows the answer to a question and R for the event the student answers the question correctly. (a) What is P (K) ? (b) What is P (RIK) ? (c) What is P (KR), as a function of N? (d) What values of N will ensure that P (K|R) >99%?
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