The problem of your way is that the three possibilities for the woman are no Laplace propabilities.

The propabilities are like this:
B-B: 50%
B-G: 25%
G-B: 25%
G-G: 0%
(which is not easily seen in your way)

What you need are Laplace propabilites, so you can add all cases where you can add all cases that meet the requirement (two boys) and devided them by the total number of possibilities.


And I'm not over complicating things. Only in the last paragraph of my last post I'm explaining MY actual (easy) solution: For both, the man and the woman, we know that one child, which we can define as the "first" child is a boy. So we just have to look at the last branch, and there we have two possibilities: "boy" or "girl", which both have a propability of 50%. Only if the second child is also a boy, we have two boys, so the propability of having two boys is 50% for both.

(Believe me, I'm working on a program that calculates propabilites of Poker hands in certain situations in Texal Hold'em with trees like you tried to make and for 5 and 7 closed cards my results are those that are on Wikipedia.