Problem:
A pair of standard 6-sided fair dice is rolled once. The sum of the numbers rolled determines the diameter of a circle. What is the probability that the numerical value of the area of the circle is less than the numerical value of the circle's circumference?
Answer Choices:
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Solution:
Let be the sum of the numbers rolled. The conditions are satisfied if and only if , that is, . Of the 36 equally likely outcomes for the roll of the two dice, one has a sum of 2 and two have sums of 3. Thus the desired probability is .
The problems on this page are the property of the MAA's American Mathematics Competitions