2011
Problem - 1448
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?
Assuming the diameter is $d$, then we have $\pi (d/2)^2 < \pi d\implies d < 4$. There are only three cases when the sum is less than $4$: $(1, 1)$, $(1, 2)$ and $(2, 1)$. Therefore the answer is $$\frac{3}{6\times 6}=\boxed{\frac{1}{12}}$$