Question

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

• A. 37/40
• B. 1/37
• C. 36/37
• D. 1/9

Answer 1

The correct option is B

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.

$P\left(A_1\right)=\frac{9}{10},P\left(A_2\right)=1-\frac{9}{10}=\frac{1}{10},P\left(\frac{E}{A_1}\right)=1$,

Then

$P\left(\frac{E}{A_2}\right)=\frac{1}{4}$

$\therefore$ Required probability

= $P\left(\frac{A_2}{E}\right)=\frac{P\left(A_2\right)P\left(\frac{E}{A_2}\right)}{P\left(A_1\right)P\left(\frac{E}{A_1}\right)+P\left(A_2\right)P\left(\frac{E}{A_2}\right)}=\frac{1}{37}$