Let, , and be the probabilities that are defined below,
The probability of student answer is .
The probability of student guesses is .
The probability of student answers correctly is .
The probability that the student knows the answer, if he answered it correctly that is ,
The probability that student knows the answer is,
The probability that the student answer correctly, given that he knows the answer,
The probability that student guess the answer is,
The probability that the student answer correctly, given that he guesses,
Put these values in equation (1),
Thus, the required probability is .