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%?