Question

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?

$\dfrac{1}{10}$

$\dfrac{1}{6}$

$\dfrac{1}{5}$

$\dfrac{1}{3}$

$\dfrac{1}{2}$

Solution:

Because the marbles left for Cheryl are determined at random, her two marbles are equally likely to be any pair. Fixing her first marble, the second is equally likely to be any of the $5$ remaining marbles.

Exactly one of those $5$ matches the first marble in color, so the probability is $\dfrac{1}{5}.$

Thus, the correct answer is C.

2015 AMC 12A Problem 9

Solution:

Problem 9 in Other Years