In a competitive examination, an examinee either guesses or copies or knows the answer to amultiple 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 the answer is correct, given that he copiedit, is `1/8`. Find the probability that he knows the answer to the question, given that he correctly answered

Explanation

`E_{1}` = answer is guessed,

`E_{2}` = answer is copied

`E_{3}` = examinee knows the answer.


`therefore P(E_{1})=frac{1}{3}, P(E_{2})=frac{1}{6}, P(E_{3})=1-frac{1}{3}-frac{1}{6}=frac{6-2-1}{6}=frac{1}{2}`


`{A}`= examinee answers correctly


Let only one of the multiple answers is correct.


`P(A / E_{1})=` Probability of answering correctly by guessing `=frac{1}{4}`


`P(A / E_{2})=` Probability of answering correct by copying `=frac{1}{8}`


`P(A / E_{3})=` Probability of answering correctly by knowing `=1`

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