Problem:
A box contains 2 red marbles, 2 green marbles, and 2 yellow marbles. Carol takes 2 marbles from the box at random; then Claudia takes 2 of the remaining marbles at random; and then Cheryl takes the last 2 marbles. What is the probability that Cheryl gets 2 marbles of the same color?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Because the marbles left for Cheryl are determined at random, the second of Cheryl's marbles is equally likely to be any of the 5 marbles other than her first marble. One of those 5 marbles matches her first marble in color. Therefore the probability is .
OR
Because all the choices are made at random, Cheryl is equally likely to take any of the possible pairs of marbles. Exactly 3 of these are pairs of same-colored marbles. Therefore the requested probability is .
The problems on this page are the property of the MAA's American Mathematics Competitions