Question: 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

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(R given K)/?

(d) What values of N will ensure that P(K given R) > 99%?

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