In a test, an examinee either guesses or copies or knows the answer to a multiple choice question with four choices. The probability that makes a guess is13 . The probability that he copies is 16 and the probability that his answer is correct given that he copied it is18 . The probability that he knew the answer to the question given that he correctly answered it, is

Let E1  be the event that the answer is guessed, E2  be the event that the answer is copied, E3  be the event that the examinee knows the answer and E be the event that the examinee answers correctly.Given P(E1)=13,P(E2)=16 assume that events, E1,E2&E3 are exhaustive.∴P(E1)+P(E2)+P(E3)=1∴P(E3)=1−P(E1)−P(E2)=1−13−16=12Now, P(EE1)= probability of getting correct answer by guessing = 14 (since 4 alternatives)P(EE2)=  probability of answering correctly by copying =18And P(EE3)=  probability of answering correctly by knowing = 1Clearly, (E3E) is the event he knew the answer to the question that he correctly answered it. Using Baye’s theorem P(E3E)  = P(E3).P(EE3)P(E1).P(EE1)+P(E2).P(EE2)+P(E3).P(EE3)=12×113×14+16×18+12×1=2429  by Bayes' theorem