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Question: Answered & Verified by Expert
In an entrance test there are multiple choice questions. There are four possible answers to each question of which one is correct. The probability that a student knows the answer to a question is $90 \%$. If he gets the correct answer to a question, then the probability that he was guessing, is
MathematicsProbabilityJEE Main
Options:
  • A $\frac{37}{40}$
  • B $\frac{1}{37}$
  • C $\frac{36}{37}$
  • D $\frac{1}{9}$
Solution:
1608 Upvotes Verified Answer
The correct answer is: $\frac{1}{37}$
We define the following events :
$A_1$ : He knows the answer.
$A_2$ : He does not know the answer.
E: He gets the correct answer.
then $P\left(A_1\right)=\frac{9}{10}, P\left(A_2\right)=1-\frac{9}{10}=\frac{1}{10}, P\left(\frac{E}{A_1}\right)=1$,
$P\left(\frac{E}{A_2}\right)=\frac{1}{4}$
$\therefore$ Required probability
$=P\left(\frac{A_2}{E}\right)=\frac{P\left(A_2\right) P\left(E / A_2\right)}{P\left(A_1\right) P\left(E / A_1\right)+P\left(A_2\right) P\left(E / A_2\right)}=\frac{1}{37}$.

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