That's true, but it doesn't imply boys and girls have the same number of brothers. As a commenter in the op pointed out, if families keep having children until

That's true, but it doesn't imply boys and girls have the same number of brothers. As a commenter in the op pointed out, if families keep having children until they have a son, no boys have any brothers and all girls have exactly one brother. I think if they keep having kids until they have a girl, though, for gors and boys you have a .5 chance no brother, .25 1 brother, and so on.