HMMT 2015 G1

Let $R$ be the rectangle in the Cartesian plane with vertices at $(0,0),(2,0),(2,1)$, and $(0,1)$. $R$ can be divided into two unit squares, as shown.

Pro selects a point $P$ uniformly at random in the interior of $R$. Find the probability that the line through $P$ with slope $\frac{1}{2}$ will pass through both unit squares.