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Juan and Amal's Dice

Source:

January 2, 2009
probability

Problem Statement

Juan rolls a fair regular octahedral die marked with the numbers 1 1 through 8 8. Then Amal rolls a fair six-sided die. What is the probability that the product of the two rolls is a multiple of 3 3? <spanclass=′latex−bold′>(A)</span> 112<spanclass=′latex−bold′>(B)</span> 13<spanclass=′latex−bold′>(C)</span> 12<spanclass=′latex−bold′>(D)</span> 712<spanclass=′latex−bold′>(E)</span> 23 <span class='latex-bold'>(A)</span>\ \frac{1}{12} \qquad <span class='latex-bold'>(B)</span>\ \frac{1}{3} \qquad <span class='latex-bold'>(C)</span>\ \frac{1}{2} \qquad <span class='latex-bold'>(D)</span>\ \frac{7}{12} \qquad <span class='latex-bold'>(E)</span>\ \frac{2}{3}
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