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 copies it is 1 8 . The probability that his answer is correct, given that he guesses it is 1 4 . The probability that he knew the answer to the question given that he correctly answered, is

Question

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 copies it is 1 8 . The probability that his answer is correct, given that he guesses it is 1 4 . The probability that he knew the answer to the question given that he correctly answered, is, 24 31, 17 24, 24 29, 29 31

MARKS App · Accepted Answer

Let E 1 , E 2 and E 3 are the events that the examinee guesses, copies and knows the answer and E is the event that he answers correctly. Then, P E 1 = 1 3 , P E 2 = 1 6 and P E 3 = 1 - 1 3 + 1 6 = 1 2 ∴ Required probability = P E 3 E = P E E 3 · P E 3 P E E 1 · P E 1 + P E E 2 · P E 2 + P E E 3 · P E 3 = 1 × 1 2 1 4 × 1 3 + 1 8 × 1 6 + 1 × 1 2 = 2 4 2 9

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