A pair of six-sided dice are labeled so that one die has only even numbers (two each of , , and ), and the other die has only odd numbers (two each of , , and ). The pair of dice is rolled. What is the probability that the sum of the numbers on the tops of the two dice is ?
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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.