Problem 3: The height of \(\triangle {XYD} \) must be at most 4.
Shading all the points that work, we can find the area of the shaded region over the area of the entire triangle.
The area of the entire triangle is 36, and the area of the shaded region is 20.
Thus the probability is \({20 \over 36 } = \color{brown}\boxed{5 \over 9}\)
Here is the image:
Note: You will get the same answer if you swap the height and width of the triangle.
