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AnotherGoodName 4 days ago

Because it's entirely dependent on sampling assumptions. Go to a random house where there's two children, one of which randomly opens the door. Each bb, gg, bg, gb is equal probability and a random child opens the door.

Now if you see a boy disregard that since you can't make the statement that one is a girl.

If you see a girl go ahead and make the statement "a family has two children. You're told that at least one of them is a girl.

What is the probability now?

You have twice the chance of making that statement if you encounter a gg family over a bg/gb family right since there's one of two girls possibly answering the door amongst those families.

So 50% chance of that statement being enabled from a gg family, 25% chance coming from a bg family, 25% chance of coming from a gb family. Which means 50% chance the other child's a girl and 50% chance the other childs a boy.

The probabilities here are entirely dependent on details of the sampling which is not made explicit here.