# Statistics puzzler

Richard J. Dudley rdudley at nrc.uab.edu
Wed Oct 29 12:06:05 EST 1997

```This is for the stats junkies out there.

A friend of mine was presented with the following problem in a job
interview:

You are given 50 black, and 50 white marbles.  Your job is to separate
them into two urns so that there is the greatest chance of picking a
white marble.

Her answer, which is apparently the correct one, was to put only one
white marble in on urn, and the rest of the marbles in the other urn,
thus giving an approx. 75% chance of selecting a white marble (by adding
the simple probabilities of 50% chance of selecting a 100% success, plus
50% chance of selecting a 50% success rate).

That sounded fishy to me.  I argued that the greatest chance is still
only 50%, because the urns represent two separate populations of
marbles, comprising a 50% success rate, and a 25% success rate.

Is this a matter of semantics, or is one of us just wrong?

Thanks for any input!

rich

--- --- --- -- -- -- --- --- ---
* Experience is something you don't get until just after you need it. *

Richard J. Dudley (rdudley at nrc.uab.edu)
Department of Neurobiology
University of Alabama School of Medicine
http://www.nrc.uab.edu/

```