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be the probability that he knows the answer and 
be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability What is the probability that the student knows the answer given that he answered it correctly? Asked by Siddhant Last Modified
Answer Let E1 and E2 be the respective events that the student knows the answer and he guesses the answer.
Let A be the event that the answer is correct.
The probability that the student answered correctly, given that he knows the answer, is 1.
∴ P (A|E1) = 1
Probability that the student answered correctly, given that he guessed, is .
The probability that the student knows the answer, given that he answered it correctly, is given by 
.
By using Bayes’ theorem, we obtain
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