Question

In the given figure, points A, B, C and D are the centres of four circles, each having a radius of 1 unit. If a point is chosen at random from the interior of square ABCD, what is the probability that the point will be chosen from the shaded region?

Answer 1

in the figure four circle of radius 1 unit covers 1/4 portion of the each end point of the square
so the side length of the square is 2 unit
and the area of the shaded reason is
area of square - 4×(1/4portion of the 4 circles)
= 4 - 4×(1/4)×π×1×1
= 4 - π

Answer 2

Radius of circle = 1cm Length of side of square = 1 + 1 = 2cm Area of square = 2 × 2 = 4cm2 Area of shaded region = area of square – 4 × area of quadrant = 4 – 4(1/4)π(1)2 = (4 − π) cm2 Probability that the point will be chosen from the shaded region = (Area of shaded region)/(Area of square ABCD) = (4 - π)/4 = 1 - π/4R