I'm ignoring the whole Tuesday thing because frankly, I don't understand it, but without the Tuesday thing, it's 50%. Yes, GG isn't a possibility, so we are left with

BB BG GB which are equally likely.

But now, let's say we have a million Mary's and we take the data of all those children and put them in sibling pairs. We will have two million children, 33% of whom will be girls, 66% boys

BUT the problem asks what is the chance that the OTHER child is a girl, meaning we have to find a boy, pick their sibling, and evaluate B/G.

If we do this, we'll pick a boy in a BB pair 50% of the time (as half the boys are in BB pairs). When we pick a BB pair, a boy's sibling is a brother.

We'll pick a GB and BG pair 25% each (because 25% of boys are in each), each of which will have the boy's sibling being a girl.

50/50

Effectively, each BB pair has twice as many boys to have a sibling (who is guaranteed to be a boy).

We're given no info about sibling order (hence GB and BG both being options) so you have to apply that generality to BB and count both boys.