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Question
Select the correct option from the given alternatives :
The probability that a student knows the correct answer to a multiple choice question is `2/3`. If the student does not know the answer, then the student guesses the answer. The probability of the guessed answer being correct is `1/4`. Given that the student has answered the question correctly, the probability that the student knows the correct answer is
Options
`5/6`
`6/7`
`7/8`
`8/9`
Solution
`8/9`
Explanation:
Let event A: Student knows the correct answer.
event A': Student guesses the answer.
event B: Answer is correct
∴ P(A) = `2/3`, P(A') = `1/3, "P"("B"/"A'") = 1/4`
Clearly, `"P"("B"/"A")` = 1
Required probability = `"P"("A"/"B")`
= `("P"("A")*"P"("B"/"A"))/("P"("A")*"P"("B"/"A") + "P"("A'")"P"("B"/"A'"))`
= `(2/3 xx 1)/(2/3 xx 1 + 1/3 xx 1/4)`
= `8/9`
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