February 7, 2000
Problem of the Month

The Urn Problem

You are presented with two urns and 10 red marbles and 10 white marbles.   You may place the marbles in the urns as you please.   Then a friend will enter the room, select an urn at random, and draw one marble from it.

How should you place the marbles in order to maximize the probability that your friend draws a white marble?

What is the probability that your friend will draw a white marble?

Solution to the Problem:

You should put one white marble in one urn and then put all the other marbles in the other urn.

The probability that your friend picks a white marble is
(1/2)(1) + (1/2)(9/19) = 1/2 + 9/38 = 28/38 or 14/19 or 73.68%.

Two people suggested that the problem did not say that ALL the marbles had to be used, so they just put white marbles in the two urns.

Therefore, the probability would be 1 or 100%.

Correctly solved by:

1. Richard Mocarski

Winchester, VA

"Weak" Solution received from:

2. Elizabeth Cotter	Oak Hill, VA
3. Jon Pence	Winchester, VA

Send any comments or questions to: David Pleacher