From: Lee Corbin (lcorbin@tsoft.com)
Date: Sat May 03 2003 - 11:32:29 MDT
Lee Daniel Crocker writes
> > (Lee Corbin <lcorbin@tsoft.com>):
> > The entire exchange between Eliezer and me concerning this
> > puzzle can be found at
> >
> > http://www.extropy.org/exi-lists/extropians.2Q01/4215.html
> >
> > I contend that statisticians tend to answer one way, and
> > mathematicians the other.
>
> If you want to know the best answer to a probability question,
> don't ask a mathematician or a statistician--ask a gambler.
But it seems to me that a "probability problem" must now be
seen as either a math problem or a statistics problem. For
example, take *this* variation:
You walk up to a random adult on the street and ask
two questions, requesting just a "yes" or "no" from
that person. Now assuming that this random person
understands English and logic, when the two questions
are (1) do you have two children? (2) do you have a
a girl?, then ignoring all cases where the answers
are not "yes" and "yes", it is a *math* problem to
determine what the probability is that he or she also
has a boy.
The answer is, of course, 2/3. There are no other answers.
Lee Daniel then refers, I think, to the problem recently
posed by Eliezer:
Eliezer wrote
> > Here's another trick question that only the true Bayesian will resolve.
> > You meet a mathematician. "How many children do you have?" you ask.
> > "Two," he replies, "and at least one of them is a boy." What is the
> > probability that they are both boys? I would *not* answer 1/3.
> A gambler would understand immediately that the answer to this
> problem depends on the motivations and methods of the one making
> the offer, just as the Monte Hall problem does, and would come
> up with both answers.
I agree that the gambler is going to utilize *everything* he knows
about our universe, including the predispositions of people who go
around asking math-like problems, and other cultural idiosyncrasies
of our civilization, and in that sense gives an extremely good
answer. Often these considerations are, IMO, relevant also to
statisticians, who are often called upon to answer real world
problems. But mathematics is different.
Lee
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