# [Taxacom] Random taxonomy

Richard Hardwick rch at skynet.be
Sat Nov 30 02:55:31 CST 2013

```"Knut Rognes" wrote

***
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.
***

I just wrote a little simulation program:-
(For each of ten thousand runs
(For each of 50 boxes
Select at random 1 of 50 labels
Look inside box
if label matches contents, record a hit
)
)

Result:

There were   36738 runs with  0 hits (36.738%)
There were   37173 runs with  1 hits (37.173%)
There were   18269 runs with  2 hits (18.269%)
There were    6050 runs with  3 hits ( 6.050%)
There were    1481 runs with  4 hits ( 1.481%)
There were     254 runs with  5 hits ( 0.254%)
There were      24 runs with  6 hits ( 0.024%)
There were      10 runs with  7 hits ( 0.010%)
There was        1 run  with  8 hits ( 0.001%)
==============================================
Thats      100000 runs

***
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?
***

Likelihood = 100-36 = 64

e.&o.e.

Richard H

Message: 12
Date: Fri, 29 Nov 2013 11:24:29 +0100
From: "Knut Rognes" <knut at rognes.no>
Subject: [Taxacom] Random taxonomy
To: <taxacom at mailman.nhm.ku.edu>
Message-ID: <00b201ceeced\$301bb6d0\$90532470\$@rognes.no>
Content-Type: text/plain;    charset="us-ascii"

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

------------------------------

```