Re: Extinction (of marbles)

[stevet@shelby.net (Stephen Throop)]

Stan Friesen wrote:

> Try a different model: in the Lancian deoposits there were about 10-12
> species of dinosaurs and more than 20 species of mammals, perhaps as
> many as 30.  Thus 300 green marbles and 100 red is more like reality.
> Now add 50 pink marbles, and 150 blue marbles, and 100 yellow ones,
> and some more of several additional colors.
> 
> Now, select 75% of the marbles.  What is the probability that all of
> *at* *least* *one* color are chosen (not necessarily red)? 
[......]
>  >  And yet this is what happened at the K/T.  Some non-random
>  > causative force was at work.
> 
> This is debatable, at best.  This is what you have to demonstrate:
> thet there *was* indeed a non-random causative force.  To do so you
> must actually perform a statistical test of the observed extinction
> pattern against the predicted extinction pattern.

Marbles!  Oh boy!

I think the easiest approach is to calculate the chances that any red
marble would be among the 25% that survive, not whether all reds would
be among the 75% that don't.

If you pick a single "survivor" from a box with 100 red marbles and 600
others, the odds are 6 to 1 that it won't be red.  However, if you pick
4, odds are slightly better than even, about 20 to 17, that one will be
a red.  If you pick 7 (1% survival), odds are about 2 to 1 that you will
have a red.

If you pick 70 (10% survival), odds are about 90 thousand to 1 that you
will have a red.  If you pick 175 (25% survival), odds are 44 trillion
to 1 that you will have at least one red.

Did I figure out the math right?  If I have applied the marble analogy
correctly, it sounds as if the KT extinctions were not random.

- Stephen Throop