Answer to the Problem of the Week

for the week of February 7, 2000

Solve the following problem between Monday and Friday. Then click on the icon below to e-mail your solution along with your name, city, and state.

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:

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