[Taxacom] Random taxonomy

Stephen Thorpe stephen_thorpe at yahoo.co.nz
Mon Dec 2 13:42:10 CST 2013


Here's a good one: Suppose that you play Russian roulette without knowing how many bullets are in the revolver (which can hold up to 6 bullets). What is the probability of shooting yourself? Do you need to know the probabilities of there being n bullets in the revolver, for n=0-6? Maybe not, as it seems that the probability of shooting yourself depends only on how many bullets are actually in the revolver, so the probability would be 0.5 if there were 3 bullets, 1 if there were 6, etc., and nothing else is relevant. Oddly, though, it would also seem to be riskier if the probability of 4, 5, and/or 6 bullets being in the revolver was high, and less risky if these were low, and yet the probability of shooting yourself doesn't seem to depend on these probabilities! I'm confused!


From: Hubert Turner <turner at casema.nl>
To: Richard Zander <Richard.Zander at mobot.org>; taxacom at mailman.nhm.ku.edu 
Sent: Monday, 2 December 2013 11:04 PM
Subject: Re: [Taxacom] Random taxonomy


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!+ Š + (-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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