SOLUTION: Two marbles are drawn (without replacement) from a bag containing 3 green, 6 yellow,and 4 red marbles. What is the probability that the marbles are of different colors?

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Question 714863: Two marbles are drawn (without replacement) from a bag containing 3 green, 6 yellow,and 4 red marbles.
What is the probability that the marbles are
of different colors?
Answer by Positive_EV(69) About Me  (Show Source):
You can put this solution on YOUR website!
The event that the marbles are different colors is the complement of the event that the marbles are the same color. Thus, calculate the probability that the marbles are the same color, then subtract this probability from 1 to find the probability they are different colors.

P(2 green) = (3/13)(2/12) = 1/26
P(2 yellow) = (6/13)(5/12) = 5/26
P(2 red) = (4/13)(3/12) = 2/26 = 1/13

P(2 of the same) = P(2 green) + P(2 yellow) + P(2 red) = 1/26 + 5/26 + 2/26 = 8/26 = 4/13.
P(2 different) = 1 - P(2 of the same) = 1 - 4/13 = 9/13.