Question

A student is writing a test and has to choose one answer from 4 when answering each question. The probability the student knows the answer is 0.7. If he does not know the answer, he randomly chooses any answer. What is the probability that the student knew the answer under the condition that the answer given by student was correct?

Answer 1

Bayes' theorem: P(A | B) = P(A & B) / P(B)

P(student knew the answer) = 0.7

P(student didn't know the answer) = 1 - 0.7 = 0.3

P(answer is correct) = P(student knew the answer and answer was correct) + P(student didn't know the answer and answer was correct)

= 0.7x1 + 0.3x(1/4)

= 0.775

P(student knew the answer | answer was correct) = P(student knew the answer and answer was correct) / P(answer was correct)

= 0.7/0.775

= 0.9032