Apoint in the figure is selected at random. find probability that the point will be in the shaded region

The probability that the point will be in the shaged region is 0.79

Explanation:

The probability of finding the random point in the shaded region is:

P = area of the shaded region / total area

The shaded region consists of two semicirles inside a square, with the diameters of the semicircles equal to the side length of the square:

Call 2r the side length, then r is the length of the radii of the semicircles:Area of one semicirle = (1/2) π r²Area of the two semicirles = 2 × (1/2) π r² = π r²Area of the square = (2r)² = 4r²P = area of the two semicirles / area of the square = π r² / 4r² = π/4 ≈ 0.79