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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 gussed answer being correct is $1 / 4$ . Given that the student has answered the question correctly, the conditional probability, that the student knows the correct answer is

Option: 1
$\frac{2}{3}$

Option: 2
$\frac{3}{4}$

Option: 3
$\frac{5}{6}$

Option: 4
$\frac{8}{9}$

Answers (1)

best_answer

Let $\mathrm{' K '}$ be the student who knows the answer. $\mathrm{' G '}$ be the student who guesses the answer. $\mathrm{' C '}$ be the event for correct answer.

$\mathrm{P(K) =\frac{2}{3} }$

$\mathrm{P(G) =\frac{1}{3} }$

$\mathrm{P(C / G) =\frac{1}{4} }$

$\mathrm{P(C / K) =1 }$

$\mathrm{P(K / C) =\frac{P(K \cap C)}{P(C)} }$

$\mathrm{ =\frac{P(K) P(C / K)}{P(K) P(C / K)+P(G) P(C / G)} }$

$\mathrm{ =\frac{\frac{2}{3} \times 1}{\frac{2}{3} \times 1+\frac{1}{3} \times \frac{1}{4}}=\frac{8}{9}}$

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