Mazra wrote:
The "Boy and a girl" vs "Girl and a boy" thing just makes zero sense to me. They're the same combination, just shifted around. 4+2 = 2+4. The order doesn't matter, does it? I get that they're two combinations, but I don't get how they, logically, count as two different combinations when they're identical.
They're not identical, as they illustrate different scenarios. You can draw paths.
Path 1 - Boy -Girl
Path 2 - Boy - Boy
Path 3 - Girl - Girl
Path 4 - Girl - Boy
Those are four unique paths, each have a probability of 25% given independant probabilities of 50% boy and girl per birth. Of those scenarios, three of them have at least one boy, but only one has two boys, hence the 1/3.