In a test, an examinee either guesses or copies or knows that answer to a multiple-choice question which has four choices. The probability that he makes a guess is and the probability that he copies is . The probability that his answer is correct, given he copied it, is . Find the probability that he knew the answer to the question, given that he answered it correctly.
Step 1: Find the probability that the examinee knows the answer.
Since, it is given that, the probability that the examinee guesses the answer is .
Also, it is given that, the probability that the examinee copies the answer is .
We know that the sum of probabilities is always equal to .
Therefore, the probability that the examinee knows the answer is given by:
So, the probability that the examinee knows the answer is .
Step 2: Find the required probability.
Assume that, is an event that the examinee's answer is correct.
So, the probability that the examinee's answer is correct by guessing.
{Because the multiple-choice question has four choices}
The probability that the examinee's answer is correct when he knows the answer is because it is a sure event.
Since it is given that the probability that the examinee's answer is correct by copying is .
Now, apply Baye's theorem to find the probability that the examinee knew the answer given that his answer is correct.
Hence, the probability that the examinee knew the answer to the question, given that he answered it correctly is .