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 ______.

Options

• `1/40`

• `1/39`

• `1/37`

• `2/43`

Answer 1

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 `underlinebb(1/37)`.

Explanation:

We define the following events :

A₁ : He know the answer

A₂ : He does not know the answer

E : He gets the correct answer

Then, P(A₁) = `9/10`, P(A₂) = `(1 - 9)/10 = 1/10`,  `P(E/A_1)` = 1, `P(E/A_2) = 1/4`.

Therefore, the required probability is

`P(A_2/E) = (P(A_2)P(E/A_2))/(P(A_1)P(E/A_1) + P(A_2)(E/A_2))`

= `(1/10 xx 1/4)/(9/10 xx 1 + 1/10 xx 1/4)`

= `1/37`