In a test, an examinee either guesses or copies or knows the answer to a multiple choice question with four choices and only one correct option. The probability that he guess is 1
3
.The probability that he copies the
answer is 1
6
.The probability that the answer is correct, given that he copied, is 1
8
. Find the probability that he knows the answer to the question, given that he correctly answered it.
Let E1 be the event that he guess and P(E1)=1/3
let E2 bet the event that he coppies and P(E2) = 1/6
let E3 be the event that he knows the answer and P(E3)= 1-1/3-1/6 = 1/2
Let A denote the event that the answer was right.
therefore P(A/E1)=1/4 (because there are four options), P(A/E2) = 1/8 and P(A/E3) = 1 (because he knows the answer)
Now P(E3/A)= 24/29
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