Area of random right triangle

A point $(a, b)$ is chosen at random from the rectangular region $[0, 2]\times [0, 4]$. Then, the probability that the area of the region $$R=\{(x, y)\in\mathbb{R}\times\mathbb{R} : bx+ay \le ab, x, y \ge 0\}$$ will be less than $2$, equals