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 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%?

Answer 1

Answer:

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%