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 E_{1} be the event that the student knows the answer, E_{2} be the event that the student guess the answer and A be the event that the answer is correct.

Then

And

Also P(A|E_{1}) = P (correct answer given that he knows) = 1

And P(A|E_{2}) = P (correct answer given that he guesses)

Now the probability that he knows the answer, being given that answer is correct, is P(E_{1}|A).

By using bayes’ theorem, we have:

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