David Ullrich wrote: > > No SPAM wrote: > > > > Dennis Rakestraw <firstname.lastname@example.org> wrote in article > > <email@example.com>... > > [stuff deleted] > > > > > If a man says, "of my two children at least one is a boy," what is the > > > probability that both are boys? The answer, oddly, is not "50-50." > > [more stuff deleted] > > > > A finer example of sexism in mathematics will ne'er be found. > > > > If men who have one boy and one girl are as likely to start, > > "of my two children at least one is a girl" as they are to start, > > "of my two children at least one is a boy", then the answer is > > indeed 50-50. > > If we start thinking about how likely people are to say > what under what conditions then it's no longer a strictly > mathematical question. One needs to rephrase (or at least interpret) > the question > > If a man says, "of my two children at least one is a boy," what is the > probability that both are boys? > > as > > Given that a man has two children, at least one is a boy, what is the > probability that both are boys? > > or the question can't be answered.
Why not? Contrary to NO SPAM's claim, it doesn't matter how often the man says "at least one boy" when he has both a boy and a girl. *When* he says "at least one boy", the chances are 1/3 that the other is a boy. Remember, it's a *conditional* probability.
It would matter, of course, if we knew he only made the statement when he had a boy and a girl, or if we knew he only made it when he had two boys, or if we knew he was lying or something. Under *those* sorts of conditions, then indeed we have other information that would affect the probability. But no amount of information about a counterfactual such as how often he says "I have at least one girl" matters in the least.