According to the meaning of the question, when the center of the circle is on the inner boundary, the circle is just tangent to a square with 40 squares.

When a circle is in a small square, it is disjoint.

The area of this small square is

(40- 10)? =900

What is the area of a big square?

40? = 1600

So the probability of disjoint is

900/ 1600=9/ 16

So the probability of intersection is

1-9/ 16=7/ 16