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Question

# In a test an examinee either guesses or copies or knows the answer to a multiple choice question with 4 choices. The probability that he makes a guess is 1/3 & the probability that he copies the answer is 1/6. The probability that his answer is correct given that he copied it, is 1/8. Find the probability that he knew the answer to the question given that he correctly answered it.If expressed in the form of a/b (simplest form), b−a=?

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Solution

## Let define the following events:E1: Examine guesses the answer to the question.E2: Examine copies the answer to the question.E3: Examine know the answer to the question.E: answer is correctHere P(E1)=13,P(E2)=16∴P(E3)=1−(13+16)=12Since the question is a multiple choice question with four choice so the probability that the answer is correct when is guessed is P(EE1)=14Also the probability that his answer is correct, given that he copied it is 18i.e P(EE2)=18Moreover his answer is correct, given he knew the answer is a sure event, so P(EE3)=1Hence by Baye's theorem the required probability isP(E3E)=P(EE3).P(E3)∑3i=1P(EEi).P(Ei)=1.1214.13+18.16+12.1=2429

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