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?

(In reply to re: Solution: With and Without Replacement by Syzygy)

You are absolutely right.  I should have read the problem more carefully.  Same logic applies though.

P(win) = 1 - 6*[(10/25)(8/24)(7/23)] - (10/25)(9/24)(8/(23) - (8/25)(7/24)(6/(23) - (7/25)(6/24)(5/(23) = 0.66478 (without replacement)

P(win) = 1 - 6*[(10/25)(8/25)(7/25)] - (10/25)(9/25)(8/(25) - (8/25)(7/25)(6/(25) - (7/25)(6/25)(5/(25) = 0.70394 (with replacement)

Posted by Russ on 2008-09-26 13:14:43