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Mathematical problems in junior high school about calculating probability
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