Timothy and Urban play a game with two dice. But they do not use the numbers. Some of the faces are painted red and the others blue. Each player throws the dice in turn. Timothy wins when the two top faces are the same color. Urban wins when the colors are different. Their chances are even.

The first die has 5 red faces and 1 blue face. How many red and how many blue are there on the second die?

The first die has a 1/6 chance of showing blue and a 5/6 chance of showing red.

If r = the number of red faces on the second die, and b = the number of blue faces, then r = 6 - b and the second die has an (6-b)/6 chance of showing red and a b/6 chance of showing blue.

When thrown together, the dice have a 1/2 chance of showing the same color. This happens when both dice show red (5/6 * [6-b]/6) or (+) when both sides show blue (1/6 * b/6)

(5/6 * [6-b]/6) + (1/6 * b/6) = 1/2
(30 -5b)/36 + b/36 = (30-4b)/36 = 1/2
30 - 4b = 18
4b = 12
b = 3
r = 6 - b = 3

Posted by TomM on 2003-03-30 06:11:51