jmc

The point can be randomly selected anywhere inside the orange square, which has area $10\cdot 10=100$. The point satisfies the given inequality if it lies within the shaded region (the diagonal side of the shaded region is a segment of the line $2x+5y=20$). We will find its area by subtracting the area of the non-shaded region from the area of the square. The non-shaded region is a triangle with base of length 10 and height of length 4, so its area is $\frac{10\cdot 4}{2}=20$. The area of the shaded region is then $100-20=80$. So the probability that the point falls within the shaded region is $80/100=\boxed{\frac{4}{5}}$.