There was a puzzle given on the Skeptics Guide podcast on 9/13/2006 and the solution they gave the next week bothered me. (They said it was ambiguous depending on how the question was phrased).
I was googling around looking for other references to this problem and found these two:
Marilyn Ignores the Obvious Regarding Probability of Boys by Herb Weiner
Eldon Moritz rebutal to Marilyn vos Savant
After reading Eldon’s page, I realized how to rephrase the question to show the right process. Everyone is focusing on the 4 possibilities of children so let’s set up the problem that way.
There are 4 women and 4 children walking through the park. The first woman (BB) has a boy with her and a boy at home, the second woman (BG) has a boy with her and a boy at home, the third (GB) has a girl with her and a boy at home, and the fourth (GG) has a girl with her and a girl at home. A man walks up to one of the women at random and sees that there is a boy with her, and asks her how many children she has. She replies that she has 2 children. What is the probably that she has 2 boys?
Clearly, the probability is 1/2 or 50%.
