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`

Answer 1

`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`