Just need some basic knowledge of probability.

The core of this problem is a geometric problem. Find the shadow circle in the picture, which accounts for a fraction of the whole square.

And this score is the expected probability result.

Total square area =2*2=4

Area of circle =πr? Find r, that is, the diagonal of the square =2√2.

The radius of the two sectors = 1, the diameter of the circle is 2√2- 1*2, and the radius r=√2- 1.

Is the area of a circle equal to π * (√ 2- 1) of a square? /4=(3-2√2)π/4

D is the correct answer.