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?

There are only two outcomes to the game.  Win or lose.  So by definition P(win) + P(lose) = 1.  Subsequently, P(win) = 1 - P(lose).

With that said, you lose when you draw 1 of each color (RYB).

P(win) = 1 - 6*[(10/25)(8/24)(7/(23)] = 0.75652 (without replacement)

P(win) = 1 - 6*[(10/25)(8/25)(7/(25)] = 0.78496 (with replacement)

Posted by Russ on 2008-09-26 02:41:47