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

Best wishes for exam

  • 25
Just adding a part to @Tom Jose's answer..
P(E3|A) = P(knows|correct)  = ​{P(correct|knows) * P(knows) }/{P(correct)} [Baye's Theorem]

Now, P(correct) = P(correct|copied)*P(copied) + P(correct|knows)*P(knows) + P(correct|guessed)*P(guessed)
= 1/8*1/6 + 1*1/2 + 1/4*1/3 = 29/48

So, ​P(knows|correct) = 1/2 * 48/29 = 24/29.
  • 12
The correct answer should be 24/27 i guess🤔
  • 4
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