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Re: Toughest Probability Question

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On 2011-12-14, Keith Thompson <kst-u@mib.org> wrote:
> A random uniform distribution is no more valid than any other
> distribution, and there are plenty of real-world circumstances in
> which a uniform distribution is highly unlikely.

Consider, for instance, the distribution of digits in numbers.  A lot of
people are aware that the distributions of first digits are uneven; for
instance, if you took a list of "the populations of all cities in an
almanac", you would find that the first digits 1-4 were more heavily
represented than 5-9 by a fair margin.  On the other hand, if you looked
in the tens place of the same numbers, you'd probably find a very even
distribution of 0-9.

Now consider the question of the overall distribution of digits in a
large body of material.  Say, every digit anywhere in said almanac.
It should be obvious that some digits will be more common than others,
with 0 significantly less common than 1.

... Now, given that:  Take the pool of all the digits in a given almanac,
including repeated copies as separate entries in the pool.  Select two of
those digits at random.  What is the probability that they're the same?
It's not 1/10.

Real world sets are, quite often, NOT random.  In fact, random sets are
sort of an anomaly.  :)

-s
-- 
Copyright 2011, all wrongs reversed.  Peter Seebach / usenet-nospam@seebs.net
http://www.seebs.net/log/ <-- lawsuits, religion, and funny pictures
http://en.wikipedia.org/wiki/Fair_Game_(Scientology) <-- get educated!
I am not speaking for my employer, although they do rent some of my opinions.

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Re: Toughest Probability Question pete <pfiland@mindspring.com> - 2011-12-12 19:29 -0500
  Re: Toughest Probability Question Seebs <usenet-nospam@seebs.net> - 2011-12-13 04:46 +0000
    Re: Toughest Probability Question Geoff <geoff@invalid.invalid> - 2011-12-12 22:19 -0800
      Re: Toughest Probability Question Seebs <usenet-nospam@seebs.net> - 2011-12-13 09:19 +0000
        Re: Toughest Probability Question "BartC" <bc@freeuk.com> - 2011-12-13 13:43 +0000
          Re: Toughest Probability Question Keith Thompson <kst-u@mib.org> - 2011-12-13 10:27 -0800
            Re: Toughest Probability Question "BartC" <bc@freeuk.com> - 2011-12-13 19:52 +0000
              Re: Toughest Probability Question Seebs <usenet-nospam@seebs.net> - 2011-12-13 20:06 +0000
              Re: Toughest Probability Question Keith Thompson <kst-u@mib.org> - 2011-12-13 12:14 -0800
                Re: Toughest Probability Question "BartC" <bc@freeuk.com> - 2011-12-13 23:34 +0000
                Re: Toughest Probability Question Seebs <usenet-nospam@seebs.net> - 2011-12-14 00:24 +0000
          Re: Toughest Probability Question Seebs <usenet-nospam@seebs.net> - 2011-12-13 19:27 +0000
            Re: Toughest Probability Question "BartC" <bc@freeuk.com> - 2011-12-13 23:56 +0000
              Re: Toughest Probability Question Seebs <usenet-nospam@seebs.net> - 2011-12-14 00:24 +0000
                Re: Toughest Probability Question "BartC" <bc@freeuk.com> - 2011-12-14 12:12 +0000
                Re: Toughest Probability Question Seebs <usenet-nospam@seebs.net> - 2011-12-14 17:47 +0000
                Re: Toughest Probability Question gordonb.qunma@burditt.org (Gordon Burditt) - 2011-12-15 08:22 -0600
                Re: Toughest Probability Question Robert Wessel <robertwessel2@yahoo.com> - 2011-12-15 14:41 -0600
                Re: Toughest Probability Question superpollo <superpollo@tznvy.pbz> - 2011-12-15 19:14 +0100
                Re: Toughest Probability Question Keith Thompson <kst-u@mib.org> - 2011-12-14 13:12 -0800
                Re: Toughest Probability Question Willem <willem@toad.stack.nl> - 2011-12-14 21:53 +0000
                Re: Toughest Probability Question "BartC" <bc@freeuk.com> - 2011-12-14 22:35 +0000
                Re: Toughest Probability Question Willem <willem@toad.stack.nl> - 2011-12-15 09:07 +0000
                Re: Toughest Probability Question Geoff <geoff@invalid.invalid> - 2011-12-15 02:07 -0800
                Re: Toughest Probability Question Keith Thompson <kst-u@mib.org> - 2011-12-15 12:13 -0800
                Re: Toughest Probability Question Geoff <geoff@invalid.invalid> - 2011-12-15 13:03 -0800
                Re: Toughest Probability Question Seebs <usenet-nospam@seebs.net> - 2011-12-15 21:36 +0000
              Re: Toughest Probability Question Geoff <geoff@invalid.invalid> - 2011-12-13 16:35 -0800
                Re: Toughest Probability Question Seebs <usenet-nospam@seebs.net> - 2011-12-14 01:20 +0000
              Re: Toughest Probability Question Keith Thompson <kst-u@mib.org> - 2011-12-13 16:44 -0800
                Re: Toughest Probability Question Seebs <usenet-nospam@seebs.net> - 2011-12-14 01:20 +0000
                Re: Toughest Probability Question James Dow Allen <jdallen2000@yahoo.com> - 2011-12-15 02:33 -0800
                Re: Toughest Probability Question gwowen <gwowen@gmail.com> - 2011-12-15 05:38 -0800
                Re: Toughest Probability Question Thad Smith <ThadSmith@acm.org> - 2011-12-18 23:34 -0700
                Re: Toughest Probability Question Bill Reid <hormelfree@gmail.com> - 2011-12-14 07:07 -0800
    Re: Toughest Probability Question Kaz Kylheku <kaz@kylheku.com> - 2011-12-13 06:55 +0000
      Re: Toughest Probability Question Seebs <usenet-nospam@seebs.net> - 2011-12-13 09:19 +0000
    Re: Toughest Probability Question pete <pfiland@mindspring.com> - 2011-12-13 12:15 -0500
      Re: Toughest Probability Question pete <pfiland@mindspring.com> - 2011-12-13 13:20 -0500
        Re: Toughest Probability Question Peter Nilsson <airia@acay.com.au> - 2011-12-13 18:15 -0800
          Re: Toughest Probability Question pete <pfiland@mindspring.com> - 2011-12-13 21:52 -0500

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