But Plumbstar, the question is NOT "What is the probability that one of the children is a girl?" It is also not asking, "A mother gives birth to one child, and it is a girl. What is the probability that the second child will be a girl?" The question is "What is the probability that one child is a girl GIVEN THAT the other child is a girl?"
The trick here is to see that both children have already been born. They're both sitting in a room somewhere. The four possible combinations are:
Child 1 boy, Child 2 boy
Child 1 boy, Child 2 girl
Child 1 girl, Child 2 boy
Child 1 girl, Child 2 girl
We KNOW that one of them is a girl, so that immediately eliminates the first scenario. Of the remaining three, only one of them provides ANOTHER girl. That's where the 1/3 probability comes in.
Nope still dont see it
Question states one is a girl whats is the probability that the other is a girl?
Well there are two options it could be a boy or a girl, 1/2
Agreed that this could go on and on though