[Taxacom] Random taxonomy
Hubert Turner
turner at casema.nl
Mon Dec 2 04:04:17 CST 2013
Dear Taxacomers, Dear Richard,
Coincidence! I was having some fun with The Penguin Book of Curious and
Interesting Puzzles, by David Wells (1st ed., 1992; ISBN 0-14-014875-2),
and came across the following problems related to the one Knut Rognes
posed.
Problem 130: ³A correspondent writes ten letters and addresses ten
envelopes. In how many ways can all the letters be placed in the wrong
envelopes?² Answer: Bernoulli posed the problem in terms of n letters.
The general formula is:
n![1/2!-1/3!+1/4!-1/5!+ + (-1*n)/n!]
[A complete answer is in Dorrie, 1965, p. 19]
Problem 131: ³If seven letters are placed in seven envelopes randomly, how
many letters would you expect, on average, to find in the correct
envelopes?² Answer: One! The answer is independent of the number of
letters and envelopes. [Newman, 1982, p. 22]
Hubert Turner
biogeography
Naturalis Biodiversity Center, Botany dept.,
Leiden, The Netherlands
On 02/12/2013 01:21, "Richard Zander" <Richard.Zander at mobot.org> wrote:
>This is the famous "birthday problem" in combinatorics. Check any book on
>probabilistic theory.
>
>_______________________
>Richard H. Zander
>Missouri Botanical Garden
>PO Box 299
>St. Louis, MO 63166 U.S.A.
>richard.zander at mobot.org
>
>
>________________________________
>
>From: taxacom-bounces at mailman.nhm.ku.edu on behalf of Knut Rognes
>Sent: Fri 11/29/2013 4:24 AM
>To: taxacom at mailman.nhm.ku.edu
>Subject: [Taxacom] Random taxonomy
>
>
>
>Dear Taxacomers,
>
>
>
>I have a statistical problem.
>
>
>
>Consider 50 black boxes, within each is a specimen of fly. Each fly has
>been
>identified by someone, its name written on the inside of the box, but this
>is invisible to you. You cannot peek inside. Each fly belong to one of 50
>possible species.
>
>
>
>You have at your disposal the 50 possible species names for these flies,
>each name printed on an adhesive label, the supply of printed labels for
>each name is limitless.
>
>
>
>Here is the game: you affix a random label on the outside of a random box.
>
>
>
>Now the problem: What is the likelihood that you put a correct label on
>the
>box, i.e. that the name on the label matches the identity of the fly
>within?
>
>
>
>Knut Rognes
>
>Oslo, Norway
>
>
>
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>
>
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>
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>
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