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Unfair Dice

Source: AMC 12 2006B, Problem 17

February 17, 2006
ratioprobabilityfunctionanalytic geometryAMC

Problem Statement

For a particular peculiar pair of dice, the probabilities of rolling 1, 2, 3, 4, 5 and 6 on each die are in the ratio 1:2:3:4:5:6 1: 2: 3: 4: 5: 6. What is the probability of rolling a total of 7 on the two dice? <spanclass=′latex−bold′>(A)</span>463<spanclass=′latex−bold′>(B)</span>18<spanclass=′latex−bold′>(C)</span>863<spanclass=′latex−bold′>(D)</span>16<spanclass=′latex−bold′>(E)</span>27 <span class='latex-bold'>(A) </span> \frac 4{63} \qquad <span class='latex-bold'>(B) </span> \frac 18 \qquad <span class='latex-bold'>(C) </span> \frac 8{63} \qquad <span class='latex-bold'>(D) </span> \frac 16 \qquad <span class='latex-bold'>(E) </span> \frac 27
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