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Cubical Dice

Source: AMC 10 2008B Problem 20

March 1, 2008
probabilityfunctionquadraticscomplementary countingAMC

Problem Statement

The faces of a cubical die are marked with the numbers 1 1, 2 2, 2 2, 3 3, 3 3, and 4 4. The faces of a second cubical die are marked with the numbers 1 1, 3 3, 4 4, 5 5, 6 6, and 8 8. Both dice are thrown. What is the probability that the sum of the two top numbers will be 5 5, 7 7, or 9 9 ? <spanclass=′latex−bold′>(A)</span> 518<spanclass=′latex−bold′>(B)</span> 718<spanclass=′latex−bold′>(C)</span> 1118<spanclass=′latex−bold′>(D)</span> 34<spanclass=′latex−bold′>(E)</span> 89 <span class='latex-bold'>(A)</span>\ \frac {5}{18} \qquad <span class='latex-bold'>(B)</span>\ \frac {7}{18} \qquad <span class='latex-bold'>(C)</span>\ \frac {11}{18} \qquad <span class='latex-bold'>(D)</span>\ \frac {3}{4} \qquad <span class='latex-bold'>(E)</span>\ \frac {8}{9}
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