In answering a question on a multiple choice test, a student either knows the answer or guesses. Let `3/4` be the probability that he knows the answer and `1/4` be the probability that he guesses. Assuming that a student who guesses at the ans

Answer

N/a

Explanation

Let `E_(1)=` event that student knows the answer
`E_(2)=` event that student guesses the answer,
and `E=` event that his answer is correct.
`:.P(E_(1))=3/4, P(E_(2))=1/4`
`:.P(E//E_(1))=` probability that his answer is correct when he knows the answer `=1`
`P(E//E_(2))=` probability that his answer is correct
when he guesses the answer `=1/4`
Now, required probability
`P(E_(1)//E)=(P(E_(1)).P(E//E_(1)))/(P(E_(1)).P(E//E_(1))+P(E_(2)).P(E//E_(2)))`
`=(3/4xx1)/(3/4xx1+1/4xx1/4)=(3//4)/(3/4+1/16)`
`=3/4xx16/13=12/13`