If there are four buildings, red, green, gray and gray, and you pick one at random you are more likely to end up in a gray building. I guess that's where my co

If there are four buildings, red, green, gray and gray, and you pick one at random you are more likely to end up in a gray building. I guess that's where my confusion lies. I see that the chances of picking a grey building the above is 1/2, but I assert that the set of possibilities for the children is "two girls", "different genders" and "two boys". But yours is a good explanation, I see that that "different genders" state has a double chance of occurring compared to the other two states. The Wikipedia article I cited above is interesting in that in one explanation, it bases the different results on interpretation of the givens. I see the problem stated as about a specific man's state, not the chances that a randomly chosen man/family with two children has two boys. In my case, this was a misdirection in trying to understand this.