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2011 AMC 10A Question 14

AMC10 · 2011 AMC 10A

Question 14

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?
  1. $\dfrac{1}{36}$
  2. $\dfrac{1}{12}$
  3. $\dfrac{1}{6}$
  4. $\dfrac{1}{4}$
  5. $\dfrac{5}{18}$