On Tue, 19 Dec 2000, Dale Berger wrote:
> Ooops, the formula doesn't work for small n and m. Consider n=2 and
m=2.
> Each man will have at least one woman by his side no matter how you
arrange
> them, so the expected number of men that will have at least one woman by
his
> side is 2.00, and the probability of at least one woman by the side of a
> given man is 1.00. The formula says p = (2m)/(n+m-1) = (2x2)/(2+2-1) =
4/3
> = 1.33! The expected number of women by the side of a given man is
1.33.
>
> Dale Berger
I apologize for sending the wrong answer. I tried to solve this problem in
an intuitive way but what was wrong with my intuition is that I forgot
that (if n+m>2), the person sitting at one's left can never be the person
sitting at one's right. The correct answer was given by Bill Taylor in
sci.stat.math newsgroup.
kk
From [EMAIL PROTECTED] Wed Dec 20 11:43:43 2000
Date: Wed, 20 Dec 2000 11:18:54 +0200
From: Kenn Konstabel <[EMAIL PROTECTED]>
To: [EMAIL PROTECTED]
Subject: [Fwd: Re: men and women around round table]
-------- Original Message --------
Subject: Re: men and women around round table
Date: 19 Dec 2000 05:25:00 GMT
From: [EMAIL PROTECTED] (Bill Taylor)
Organization: Department of Mathematics and Statistics, University of
Canterbury, Christchurch, NewZealand
Newsgroups: sci.stat.math
References: <[EMAIL PROTECTED]>
Elvis Rodriguez <[EMAIL PROTECTED]> writes:
|> can someone help with this challenging problem??
Not very challenging. Indeed, it looks like homework.
It's a standard example of E[sum] = sum(E)
|> suppose m men and n women are sitting around a round table.
We'll assume random placement, unlike the Thurber scenario! ;-)
|> expected number of men that will have at least one woman by their
sides?
P(some particular man has at least one adjacent woman)
= 1 - P(he has two men)
= 1 - [(m-1)/(m+n-1)]*[(m-2)/(m+n-2)] (standard condtnl prob
calcn)
m(m-1)(m-2)
Thus E[number of such] = m - ----------------
(m+n-1)(m+n-2)
> Thanks in advance ( <---- Elvis didn't actually SAY this )
You're welcome.
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Bill Taylor [EMAIL PROTECTED]
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I really y = 3/ 2 + / 2 math!
v x v 1 - x
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