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This post is all correct except for the last paragraph. This property you describe is true in general, but this problem is a simpler case. It's trivial to show that E[G]/E[G+B] = 1/2 if G and B are i.i.d variables... E[G]/E[G+B] => 1/(E[G+B]/E[G]) => 1/(E[G]/E[G]+E[B]/E[G]) => 1/(1+1) => 1/2`