OK, now with 3.13M families:
# echo 'select child1_gender,count(*) from families where child2_gender = "M" and child2_day=2 group by child1_gender;' | mysql test
50.095% male. If I remove the Tuesday constraint?
# echo 'select child1_gender,count(*) from families where child2_gender = "M" group by child1_gender;' | mysql test
But you know, perhaps I'm being not literal enough. It's always possible to misencode a problem, and there's a lot of insistence that you have to handle the overlapping case of boy/boy. So, lets try a different mechanism. Lets literally do what the problem asks:
"I have two children, one of whom is a boy born on a Tuesday. What's the probability that my other child is a boy?"
For each family, if either of the children is male, return whether they are both male.
# echo 'select child1_gender=child2_gender from families where (child1_gender="M" and child1_day=2) or (child2_gender="M" and child2_day="2") ' | mysql test | sort | uniq -c | sort -n
...heh! That's kind of neat! I think I shall play with this some more.
All I ask is a chance to prove that money can't make me happy.