From: Mark Neely <accessnt@ozemail.com.au>
Date: Wed, 7 Aug 1996 18:22:35 +0800
To: cypherpunks@toad.com
Subject: The Solution: 20 Beautiful women
Message-ID: <2.2.32.19960807080312.00695a08@ozemail.com.au>
MIME-Version: 1.0
Content-Type: text/plain


Fellow Cypherpunks,

Maths was never my strong point, but this response (from my statistician
g/f) sounds convincing...but then, maybe I'm biased :)

-----8<-------

According to your friendly neighbourhood statistician (ie me) the answer can be
deterined as follows:

Suppose we have 20 beautiful women and we call them W1, W2 through to W20.  For
any given women, say Wi where 1<=i<=20, we have only two choices, choosing her
or rejecting her.  Knowing that she's beautiful anyway, we assume that:

Probability(Choosing Wi)=Probability(Rejecting Wi)=0.5

Now, let Wn where 1<=n<=20 be the most beautiful woman, then the probability of
getting the most beautiful woman is:

Probability(Getting Wn)
        =Probability(Rejecting W1) * Probability(Rejecting W2) *
                Probability(Rejecting W3) * ... * Probability(Rejecting Wn-1) *
                Probability(Choosing Wn)
        =(0.5)^(n-1) * (0.5)
        =(0.5)^n

Now we know that the value for a fraction raised to any of the valid values of n
(defined above to be 1<=n<=20) can be maximised by minimising the power to which
the fraction is raised.  So we take the minimum possible value of n, namely n=1.

Thus Probability(Getting Wn)=(0.5)^n=0.5.  This gives us the highest chance of
choosing the most beautiful woman.

This could have been done more intuitively and less rigorously by considering
the fact that when we multiply any fraction by another fraction, it always
becomes a smaller fraction (and hence our probability is reduced).

So you can see there is a moral in this story, can you not?

I pat myself on the head.  I am extremely brilliant.

She who is most luscious
___
Mark Neely - accessnt@ozemail.com.au 
Lawyer, Internet Consultant, Professional Cynic
Author: Australian Beginner's Guide to the Internet (2nd Ed.)
	Australian Business Guide to the Internet
	Internet Guide for Teachers, Students & Parents
WWW: http://www.ozemail.com.au/~accessnt