Re: Me and David C. Ullrich
- From: john_ramsden@xxxxxxxxxxxxxx
- Date: 9 Oct 2005 05:18:56 -0700
quasi wrote:
>
> On 8 Oct 2005 07:12:35 -0700, "Elmo" <elmoritz@xxxxxxxxx> wrote:
>
> >On this forum I have argued the question, "Two coins were flipped and
> >at least one is a head. What are the chances that there are two heads?"
> >
> >Many mathematicians get it confused with "The probability for two
> >heads, given at least one head?"
> >
> >I say that "given at least one head", and told, "at least one head"
> >mean two different things.
> >
> > ...
> >
> >When you accept that "given at least one" and told, "at least one" are
> >different; then it's easy to get from:
> >
> >P(hh|at least one h) = 1/3 to
> >P(hh|told "at least one h) = 1/2.
> >
>
> If information is "given", how is it given? Someone tells you,
> right? I can't think of any other way to interpret "given".
Exactly, and the natural interpretation is that this condition
is being given by the person stating the question. Even if not,
one must assume that the information is equally accurate. So,
although there may be a hairsplitting logical distinction in
how the question is framed, the salient facts are the same.
If the condition had been given by someone else, who tells lies
half the time or something, then yes it would be an different
question. But surely everyone agrees that a problem like this
must be taken how one finds it, as an abstract exercise, without
trying to read between lines and perversely imagine all kinds of
complicating factors, even if it might be appropriate to do that
in real life.
.
- References:
- Me and David C. Ullrich
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- Re: Me and David C. Ullrich
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- Me and David C. Ullrich
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