Question

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

Answer 1

Given: A, B, C, and D are the centers of four circles that each have a radius of length one unit. If a point is selected at random from the interior of square ABCD

To find: Probability that the point will be chosen from the shaded region,

In the figure we can see 4 circles of radius 1 unit.

Area of quarter circle with centre A:

Since all the circles are of the same radius, hence the area of quarter with centre B, C, D will be same as the area of circle of quarter of circle with centre A.

Hence total area covered by 4 quarter circle will be

Side of the square will be 2 units

Area of square ABCD = 4 unit²

Area of the shaded portion

We know that PROBABILITY

Hence probability of the shaded region is.