Go To Your Study Dashboard

Get Answers to all your Questions

header-bg

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.

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

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

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

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

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

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

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

Posted by

avinash.dongre

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

5 g of Na₂SO₄ was dissolved in x g of H₂O. The change in freezing point was found to be 3.82⁰C. If Na₂SO₄ is 81.5% ionised, the value of x (K

A capacitor is made of two square plates each of side 'a' making a very small angle $\alpha$

A solution of m-chloroaniline, m-chlorophenol and m-chlorobenzoic acid in ethyl acetate was extracted initially with a saturated solution of NaHCO₃ to give fraction A. The leftover organic phase was extracted with d

Trending Articles/News

anam-khan

JEE Main 2026: JCECEB invites fresh applications for Jharkhand state merit list correction

Latest Question