Date: Thu, 29 Apr 1999 16:20:52 -0700
From: Dan Gray <dgray@justin-siena.napanet.net>
To: Pinhole Listserv <pinhole@exploratorium.edu>
Subject: Re: pinhole Re: probability
Actually, I think our math friend got it right. Score one for the
mathematicians! The question, as I recall, refers to asking a woman one meets
about her sibling. That's it. Now consider a pool of 4 sets of siblings: one
brother-brother, one brother-sister, one sister-brother, one sister-sister. I
think we can agree this takes into account the combination in their appropriate
ratios (from a purely statistical point of view... I think there are in fact
more boys born than girls.... and there are other biological considerations as
well I suppose...).
If you eliminate the brothers, that leaves 4 women. Two of the women have a
brother and two have a sister.
Tat puts the odds back to 1:1
The sisters MUST count as two women, not one, since that is how it would come
out statistically given the way the question was framed.
-Dan Gray
Steven Eiger wrote:
> I disagree. You mathemeticians are too smart for your own good; you find
> it too easy to see things in an abstract sense (I say this with a sizable
> amount of jealousy). Saying "You have a female friend with one sibling"
> suggests to me that you have a real friend, a person with flesh and blood;
> a single entity, if so then she would be looking at the situation from her
> perspective and not the dual perspective of her and her sister if she had
> one, thus your first model works, the family one. Steve Eiger
>
> >Finally, a pinhole subject for the mathematicians among us! I've been
> >posing this problem to friends and relatives (my intuition says 50-50 in
> >spite of the coin analogy), and got this response from my brother, which I
> >thought was worth sharing:
> > OK, this thing has been bugging me. I think this is more complicated
> >than we've been led to believe.
> > It seems to me that there are two different problems here, that
> >consist of counting two different (but related) sample spaces. One is
> >the space of "families with two children, at least one of whom is a
> >girl," and the other is the space of "girls with one sibling."
> > If you count the families space, then indeed the number of families
> >with a boy and a girl is twice as big as the number of families with two
> >girls. And if you can show that the older child is a girl (or the
> >younger one, for that matter), then you have eliminated one quadrant and
> >the numbers even out.
> > But if you count the space of "girls with one sibling," you get a very
> >different answer. You get exactly half of them having a brother, just
> >as your intuition would expect.
> > To see this, consider a universe of 3 families: one with an older
> >brother and younger sister, one with an older sister and younger
> >brother, and one with two sisters. If you count families, you get 2
> >with brothers versus 1 without. But if you count girls, there are 4 of
> >them, 2 of whom have brothers and 2 of whom do not. The numbers are
> >different because you count both girls from the family with 2 girls.
> > The question now is which of these 2 counting schemes applies to the
> >given problem. As you described it to me, the problem was: "You have a
> >female friend who has one sibling. What is the probability that her
> >sibling is male?" It seems pretty clear to me that you are counting
> >girls here, rather than families.
> > On the other hand, if the problem was "You have a friend who has 2
> >children, at least one of which is a girl. What is the probability that
> >the other child is a boy?", then I think you are counting families. But
> >of course you can recast this question to be very similar to the other
> >one, like "What is the probability that that girl's sibling is a boy?"
> > The real lesson of all this, I would say, is that word problems can be
> >very subtle. The thing that really irks me about Marilyn Vos Savant
> >(who I think popularized this problem) is that she only talks about one
> >interpretation of her problems, which she loudly proclaims to be the
> >correct interpretation. In this case, it sounds to me like she latched
> >onto the wrong interpretation.
> >
> >
> >
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>
> Steven Eiger, Ph.D.
>
> Departments of Biology and the WWAMI Medical Education Program
> Montana State University - Bozeman
> Bozeman, MT 59717-3460
>
> Voice: (406) 994-5672
> E-mail: eiger@montana.edu
> FAX: (406) 994-3190
>
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