# [Taxacom] Random taxonomy

Dan Lahr dlahr at ib.usp.br
Fri Nov 29 07:34:22 CST 2013

```I have not given much thought to this, but is an interesting question.

The complication is that your events are NOT independent, that is, being
wrong in box X mandates that you will be wrong 2 more times - you have one
extra label that should go with box X but wont, plus you have a fly in box
Y that will not receive the correct label that is in box X.

IF we assume the events ARE independent, in classical probability, the
chance that you would be correct in ALL boxes would be:

1. The chance of being correct each time 1/50.
2. This will happen 50 times so 1/50ˆ50

That is about 8.9 x 10ˆ84.  The estimated number of atoms in the universe
is 10ˆ80, just for comparison.

The lack of independence will only decrease the probability of being right
in all boxes, the probability is already so ridiculously small that there
is no point in going the extra mile to figure this out. It is close to
impossible to get all 50 boxes right.

Where it matters in my view is knowing the probability of being correct in
AT LEAST one box, or in two, or three and so on.  If the independence
assumption were correct, it would be 1/50ˆ2, 1/50ˆ3 and so on.  But this is
not a good approximation, it may perhaps work as a decent flat prior
probability.  Certainly someone with a better Bayesian background would be
a lot of help for you.

If you do figure it out, please let me know!

cheers,

Dan

__________________________________
Daniel J. G. Lahr
PhD, Assist. Prof.
Dept of Zoology, Univ. of Sao Paulo, Brazil
Office number: + 55 (11) 3091 0948
http://www.ib.usp.br/zoologia/lahr/

On Fri, Nov 29, 2013 at 8:24 AM, Knut Rognes <knut at rognes.no> wrote:

> 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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>

```