I should know better than to start this sort of thing with a crowd as argumentative as NRO readers.

Still, though I’m getting a lot of propositional calculus, nobody has addressed my empirical result.

Come on, show me where I’m wrong. I’m popping out millions of two-child families with sex and day of week randomly, independently assigned for each child. I’m tallying how many families have a boy born on a Tuesday; and what proportion of them have a second boy.

I just ran it again, generating ten million families. 1,377,772 of them had a boy born on a Tuesday; 663,476 of them had a second boy. Ratio: 0.481557180723661, within a thin whisker (0.016 percent) of 13/27.

So out of ten million random-random two-child families, of those with a son born on a Tuesday, 13/27 had the other child a son too.

Sure, I understand it’s counterintuitive. That’s the fun of these things. But where would I be wrong, if I were a betting man (which, today, I’m very glad I’m not) in going with 13/27 on the proposition as offered?

No more 45-line Bayesian algorithms, please; just tell me where my empirical reasoning is wrong.