### Instruction: A point $(x,y)$ is randomly picked from inside the rectangle with vertices  $(0,0)$, $(3,0)$, $(3,2)$, and $(0,2)$.  What is the probability that  $x < y$?### Response: I need to find the area of the region inside the rectangle where $x < y$, and divide it by the total area of the rectangle.
The total area of the rectangle is $3 \times 2 = 6$.
The region where $x < y$ is a triangle with vertices $(0,0)$, $(0,2)$, and $(2,2)$.
The area of this triangle is $\frac{1}{2} \times 2 \times 2 = 2$.
So the probability that $x < y$ is $\frac{2}{6} = \frac{1}{3}$.