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Odd Dice

Source: 2012 AMC10A Problem #9

February 8, 2012
probabilityAMC

Problem Statement

A pair of six-sided fair dice are labeled so that one die has only even numbers (two each of 22, 44, and 66), and the other die has only odd numbers (two each of 11, 33, and 55). The pair of dice is rolled. What is the probability that the sum of the numbers on top of the two dice is 77?
<spanclass=′latex−bold′>(A)</span> 16<spanclass=′latex−bold′>(B)</span> 15<spanclass=′latex−bold′>(C)</span> 14<spanclass=′latex−bold′>(D)</span> 13<spanclass=′latex−bold′>(E)</span> 12 <span class='latex-bold'>(A)</span>\ \dfrac{1}{6} \qquad<span class='latex-bold'>(B)</span>\ \dfrac{1}{5} \qquad<span class='latex-bold'>(C)</span>\ \dfrac{1}{4} \qquad<span class='latex-bold'>(D)</span>\ \dfrac{1}{3} \qquad<span class='latex-bold'>(E)</span>\ \dfrac{1}{2}
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