In answering a question on a multiple choice test, a student either knows the answer or guesses. Let 3/4 be the probability that he knows the answer and 1/4 be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability 1/4. What is the probability that the student knows the answer given that he answered it correctly?

Given: let E1 be the event that the student knows the answer, E2 be the event that the student guess the answer and A be the event that the answer is correct.

Then


And


Also P(A|E1) = P (correct answer given that he knows) = 1


And P(A|E2) = P (correct answer given that he guesses)


Now the probability that he knows the answer, being given that answer is correct, is P(E1|A).


By using bayes’ theorem, we have:







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