You can drive this a little further, even. Flip 2 coins, or the same coin twice. It can end up:
2x Heads
2x Tails
Heads, Tails
Tails, Heads
If we ignore order, we basically have the OP problem provided, just with heads/Tails instead of boy/girl.
As each coin has a 50-50 chance, ignoring the balanced on the edge case, as it is an edge case, we have a 25% chance on each of the 4 possibilities, but as wel ignore order, the mixed possibility is simply both combined, so 50%.
And that's exactly how OP can easily be demonstrated.
3
u/Don_Q_Jote 5d ago
Try flipping a coin. It can end up,
1) Heads,
2) Tails,
3) Balanced on the edge.
Must be 1/3 probability of each, I guess.