A bin contains 25 balls: 10 red, 8 yellow, and 7 blue. We draw three balls at random (without looking!) from the bin, and we will say that we "win" if our three balls represent exactly two colors. (That is, we "win" if we draw two balls of one color and another ball of a different color.)
What is the probability of winning in this particular game?
The probability that all 3 colors would be drawn is
10/25 * 8/24 * 7/23 * 3! = 28/115
The probability that all 3 balls would be red is
10/25 * 9/24 * 8/23 = 6/115
The probability that all 3 balls would be yellow is
8/25 * 7/24 * 6/23 = 14/575
The probability that all 3 balls would be blue is
7/25 * 6/24 * 5/23 = 7/460
Then, the probability that two are of one color and one is of another is just 1 minus the total of the above. This comes out to 1529/2300 or about 0.6647826086956521738.

Posted by Charlie
on 20080925 12:21:40 