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Re: The probability of boys
Posted:
Dec 17, 1997 3:02 AM
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David Ullrich wrote:
>
> No SPAM wrote:
> >
> > Dennis Rakestraw <drakestraw@hotmail.com> wrote in article
> > <882203102.2049048581@dejanews.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.
--
<J Q B>
x
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