2012 AMC 10A Problem 9

A pair of six-sided fair dice are labeled so that one die has only even numbers (two each of

2,

4,

and

6

), and the other die has only odd numbers (two each of

1,

3,

and

5

). The pair of dice is rolled. What is the probability that the sum of the numbers on the tops of the two dice is

7?

Show solution

Solution

The pairs of numbers that sum to

7

are

(2, 5), (4, 3), \text{ and } (6, 1).

There is a

\dfrac{1}{3} \cdot \dfrac{1}{3} = \dfrac{1}{9}

chance that we get any of these pairs. There are

3

pairs, which means that the total probability that the rolls sum to

7

3 \cdot \dfrac{1}{9} = \dfrac{1}{3}.

Thus, D is the correct answer.

Tagged: dice (probability) · casework