On Mon, 12 Jun 2006, James Propp wrote:
"A family has two children, at least one of whom is a boy; what is the probability that both are boys?"
and
"A family has two children, at least one of whom is a boy named Bartholomew; what is the probability that both are boys?"
have different answers.
That doesn't sound right to me. Flip two coins. Flip again if you get TT. Then you have: P(HT)=0.33 P(TH)=0.33 P(HH)=0.33 Now name one of the heads Bart. How did that change P(HH)=0.33? If you told me the *first* one was Heads (IOW, reflip if either TT or TH comes up), then we'd have: P(HT)=0.5 P(HH)=0.5 But I don't see how naming one of the Boys/Heads (which is guaranteed to exist) changes probabilities. (Heh, but keep in mind that I can be stubborn. When I read the Wikipedia article on the Monty Hall problem, I argued stridently that it was wrong, and coded it up in Perl to prove that I was... wait, why does it keep coming up with *their* answer? :) ) -J