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 the gets the correct answer to a question, then find the probability that he was guessing.

Options

A. `(1)/(9)`
B. `(36)/(37)`
C. `(1)/(37)`
D. `(37)/(40)`

Answer

C

Explanation

Consider the following events :
`E_(1) to ` He knows the answer, `E_(2) to `He guesses the answer
`A to ` He gets the correct answer.
We have,
`P(E_(1))=(90)/(100)=(9)/(10),P(E_(2))=(1)/(10)`,
`P(A//E_(1))=1, P(A//E_(2))=(1)/(4)`
`therefore` Required probability `=P(E_(2)//A)`
`=(P(E_(2))P(A//E_(2)))/(P(E_(1))P(A//E_(1))+P(E_(2))P(A//E_(2)))`
`=((1)/(10)xx(1)/(4))/((9)/(10)xx1+(1)/(10)xx(1)/(4))=(1)/(37)`