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From: levy@princeton.UUCP
Newsgroups: net.math
Subject: Re: Another counterintuitive problem in probabilities
Message-ID: <8@princeton.UUCP>
Date: Mon, 22-Aug-83 01:52:31 EDT
Article-I.D.: princeto.8
Posted: Mon Aug 22 01:52:31 1983
Date-Received: Mon, 22-Aug-83 10:53:42 EDT
References: <221@turtleva.UUCP>
Organization: Princeton University
Lines: 17

Suppose someone has ten (real) numbers, written on slips of paper.  This
person will draw the slips one by one, and read the numbers aloud.  It is
your task to spot the highest number *as soon as it is read*, i.e. if you
let it go, you lose.  Of course you don't know a priori what the numbers
are, so if you claim that one of the first numbers is the highest, you
really don't have much information to go by, and if you wait until near
the end, chances are you're going to miss the highest number.

The question is: what is the best strategy to guess the highest number?
What is the probability that it will work?  What happens if instead of
ten numbers you take a hundred, or one thousand, etc.?

The answer to all three questions is very surprising.  If you know it
already, ou if you found it in three seconds, *don't post it*!  Answer
by mail.

			-Silvio Levy