Probability 4 Question 24
24. In a test an examinee either guesses or copies of knows the answer to a multiple choice question with four choices. The probability that he make a guess is and the probability that he copies the answer is . The probability that his answer is correct given that he copied it, is . Find the probability that he knew the answer to the question given that he correctly answered it.
(1991, 4M)
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Solution:
- Let
and be the events defined as
We have,
Since,
If
i.e.
It is given that,
and
By Baye’s theorem, we have