Question 2
A point $P$ is chosen at random in the interior of a unit square $S.$ Let $d(P)$ denote the distance from $P$ to the closest side of $S.$ The probability that $\frac{1}{5} \le d(P) \le \frac{1}{3}$ is equal to $\frac{m}{n},$ where $m$ and $n$ are relatively prime positive integers. Find $m + n.$