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MathematicsMathematics
14 May, 19:33

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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  1. 14 May, 20:08
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    Step-by-step explanation:

    a) P (K) = 0.7

    b) P (R|K) = 1

    c) P (K|R) = P (KnR) / P (R)

    = P (K) x P (R|K) / (P (K) x P (R|K) + P (K') P (R|K')

    = 0.7 x 1 / (0.7 x 1 + (1-0.7) x 1/N)

    = 0.7 / (0.7 + 0.3/N)

    d) P (K|R) > 0.99

    0.7 / (0.7 + 0.3/N) > 0.99

    N > 42.86

    N = 43 will be the value of N that will ensure that P (K|R) >99%
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