Area Between Curves: Videos & Practice Problems

Two points $A$ and $B$ are chosen independently and uniformly at random, one on each of two adjacent sides of a square of side length $2$. Let $x$ be the distance from the shared vertex to point $A$ along one side, and $y$ the distance from the shared vertex to point $B$ along the other side ($x,y\in [0,2]$). The area of the right triangle with vertices at the shared vertex and the two chosen points is $\frac{1}{2}xy$. What is the probability that the area of the right triangle is less than $1$?