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From: tomj@chinet.UUCP (Tom)
Newsgroups: net.math,net.crypt
Subject: Interesting Problem
Message-ID: <317@chinet.UUCP>
Date: Wed, 12-Feb-86 22:03:01 EST
Article-I.D.: chinet.317
Posted: Wed Feb 12 22:03:01 1986
Date-Received: Sun, 16-Feb-86 00:01:09 EST
Distribution: na
Organization: chinet, Public Access UN*X, Chicago, IL
Lines: 34
Keywords: Probability, Number Theory, Combinatorics

This problem originally appeared (to the best of my knowledge) as one of
ten questions on Part II (of X) Actuarial Exams back when it was essay-
format rather than multiple-choice.  The test was three hours long.
 
	Question:	Given a collection of w white balls and b black
			balls drawn blindly from an urn, what is the
			most probable (mode) number of changes of color?
			(_e.g._ Given two white balls and one black
			ball, the most probable number of changes of
			color is 1:  
		
				001 -- one change
				010 -- two changes
				100 -- one change
		
			P{1 change|2 white, 1 black} = 2/3
 
I have not yet solved this problem.  Expanding the problem, given m objects
of type I, and n objects of type II, what is the probabilistic distribution
of the number of changes of type?
 
[This seems to have some cryptanalytic importance to me.  Does it?]
 
_____
Tom Johnston		...ihnp4!chinet!tomj
 
	"You're one of US now  --  a SOLDIER in the SACRED WARS..."
	"SACRED WARS?  Whad's nad?..."
	"I can't TELL you that."
	"Why dot?"
	"They're SECRET Sacred Wars."
 
Disclaimer:  I voted; but we were in Chicago, and you have to be dead to vote
	     there.