In the given figure, A, B, C and D are centres of four circles that have a radius of 1 unit. If a point is selected at random from interior of square ABCD, then what is the probability that it lies in the shaded region

Explanation

Area of the shaded region = Area of the square -4 times Area of the sector of the circle

area of a circle `=(2 times 2)-4 times frac{1}{4}(pi)(1)^{2}=4-pi`

Required probability`= frac{ Area of shaded region }{ Area of square }=frac{4-pi}{4}`