Message-Id: <l03102800b34e3141fee0@[153.90.236.25]>
In-Reply-To: <v01540b00b34d76fe4247@[209.204.150.77]>
Date: Thu, 29 Apr 1999 10:08:56 -0600
To: "Pinhole Listserv" <pinhole@exploratorium.edu>
From: Steven Eiger <eiger@montana.edu>
Subject: Re: pinhole Re: probability
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