Question 46
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.
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.