Let total student = x .
Number of student who think they know the answer = (20/100)*x = x/5
Number of student who knows correctly = (1/2)*(x/5) = x/10
number of students who knows wrong answer = (1/2)*(x/5) = x/10
Remaining candidate = x-(x/5) = 4x/5
probability of answering correctly by remaining candidate = (1/4)*(4x/5) = x/5 ......[as 1 out of 4 option is correct]
P(answer knew / aswered correctly ) = P(answer knew ∩ answered correctly) / P(answered correctly)
= (x/10) / { (x/10) + (x/5) } = 1/3
