In a test, an examinee either guesses or copies or knows the answer to a multiple choice question with four choices. The probability that he makes a guess is 1/3 and the probability that he copies the answer is 1/6. The probability that his answer is correct given that he copied it is 1/8. Find the probability that he knew the answer to the question, given that he correctly answered it.

Explanation

Leg G denote the event the examinee gueses, C denote the event the examinee copie and K the event the examinee knows the answer. Then given that
`P(g)=1//3,P(C)=1//6`
`andP(K)=1-1//3-1//6=1//2.`
Here, it has been assumed that the events G, C and K are mutually exclusive and exhaustive. If R denotes the event that the answer ir right, then
`P(R//G)=14,` as out of the four choices only one is correct. `P(R//C)=1//8` (given).Also P(R/K)=1, since the probability of answering correctly wien one knows the answer is equal to 1.
Now, by Bayes's theorem, the probability that he knows the answer, given that he answered correctly is given by
`P(K//R)=(P(K)P(R//K))/(P(G)P(R//G)+P(C)P(R//C)+P(K)P(R//K))`
`=((1//2)xx1)/((1//3)(1//4)+(1//6)(1//8)+(1//2)xx1)=(24)/(29)`