I'm trying to pull some old Olympiad questions for some students, but I can't get a handle on this one. I'd really like to include it, though. In answering general knowledge questions (framed so that each question is answered yes or no), the teacher's probability of being correct is A and a pupil's probability of being correct is B or G according as the student is a boy or a girl. The probability of a student agreeing with the teacher is 1/2. Find the ratio of boys to girls in the class. Now, I'm new to Olympiad questions, but the best I can do is: Let x = P(selecting boy) such that: x = #boys / (#boys + #girls) ... x#boys + x#girls = #boys ... x#girls = (x-1)#boys ... #boys / #girls = x/(x-1) = r is the desired ratio. Then P(agree) = P(teacher correct & student correct | boy) + P(teacher correct & student correct | girl) + P(teacher incorrect & student incorrect | boy) + P(teacher incorrect & student incorrect | girl) 1/2 = A*x*B + A*(1-x)*G + (1-A)*x*(1-B) + (1-A)*(1-x)*(1-G) But there's not much else I can do to simplify that, or to find x. Any suggestions? Thanks.