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.

Explanation

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(A_(1))=9//10,P(A_(2))=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))P(E//A_(2)))`
`=(1/10xx1/4)/(9/11xx1+1/10xx1/4)=1/37`