-----Original Message----- From: math-fun-bounces+andy.latto=pobox.com@mailman.xmission.com On Behalf Of James Propp Sent: Monday, June 12, 2006 11:11 PM To: math-fun@mailman.xmission.com Subject: [math-fun] Re: Error in Scientific American math puzzle.
The way I usually teach this topic in introductory probability classes is that (under assumptions that need to be made explicit but are very reasonable), the question
"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's a really nice version of the puzzle. The (very slight) flaw is that in the second case, the answer is not "1/2", but "very slightly less than 1/2". It's important that you present the problem with an unusual name, like Bartholemew, since the more common the name, the greater the deviation from 1/2. Since I only know of one person named Bartholemew (and he has two sisters, Maggie and Lisa, so he doesn't affect the odds in this problem), the approximation is pretty good in this case. Andy Latto andy.latto@pobox.com
I learned this gimmick (giving the boy a name) from Charles Grinstead or Peter Doyle (I'm not sure which).
Jim Propp