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 |