This is a question from my mathematics textbook. I am studying conditional probability and know how to solve this problem. Where I get confused is that my book treats the cases:(boy, girl) & (girl, boy) differently, i.e., as if they are not the same. Why does the order matter here? By the way, I know that the answer is $\frac13$ if you do it this way. And according to my understanding it should be $\frac12$ as I don't see why the possibilities of the family having (boy, girl) & (girl, boy) are different, although they mean the same thing.
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2This is something that has already featured on MSO. (Many times.) In a family with two children, what are the chances, if one of the children is a girl, that both children are girls? Please go through this post and any linked posts and maybe you will find what you are looking for. – Apr 22 '23 at 08:01
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1Shortly, you don't need to consider the cases (boy, girl) and (girl, boy) separate, you can consider them one case, but the fact is that that case is then twice as likely as any of the cases (boy, boy) or (girl, girl). – Apr 22 '23 at 08:03
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1https://en.wikipedia.org/wiki/Boy_or_Girl_paradox – Jean-Claude Arbaut Apr 22 '23 at 08:04