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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.

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.