Answer:
- 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 r²
- Area of the two semicirles = 2 × (1/2) π r² = π r²
- Area of the square = (2r)² = 4r²
- P = area of the two semicirles / area of the square = π r² / 4r² = π/4 ≈ 0.79
