Because if you select a random family from the set of familes with two children, the 4 permutations (BB,BG,GB,GG) are equally likely, at 25% each, so it's the s

Because if you select a random family from the set of familes with two children, the 4 permutations (BB,BG,GB,GG) are equally likely, at 25% each, so it's the simplest way to model it. If you model it in your way with 3 possible scenarios you'll find that the probabilities are BB: 25%, one of each: 50%, GG: 25%, and dealing with those differing probabilities is harder than just splitung the one of each scenario into two. Try it with 2 coins flipped at the same time and you'll see it's the case. You'll get 2 unmatching coins about twice as often as you get either HH or TT.