2019 AMC 8
Complete problem set with solutions and individual problem pages
The faces of each of two fair dice are numbered , , , , , and . When the two dice are tossed, what is the probability that their sum will be an even number?
- A.
- B.
- C.
- D.
- E.
Solution 1
We have dice with evens and odds on each die. For the sum to be even, the 2 rolls must be odds or evens.
Ways to roll odds (Case ): The total number of ways to obtain odds on 2 rolls is , as there are possible odds on the first roll and possible odds on the second roll.
Ways to roll evens (Case ): Similarly, we have ways to obtain 2 evens. Probability is , or .
Solution 2
We count the ways to get an odd. If the sum is odd, then we must have an even and an odd. The probability of an even is , and the probability of an odd is . We have to multiply by because the even and odd can be in any order. This gets us , so the answer is .
