jmc

We draw the region and mark off the area where $x+y\le 4$:

The area of the rectangle is 18. The area of the shaded region, a trapezoid, is $\frac{1}{2}(1+4)\cdot 3=\frac{15}{2}$. The probability that the point ends up in the shaded region is then $\boxed{\frac{5}{12}}$.