Question

@whpalmer4 A point in the figure is selected at random. Find the probability that the point will be in the shaded region
https://pwnd9373-ndscholarship-ccl.gradpoint.com/Resource/630568,72F,0,0,0,0,0/Assets/testitemimages/geometry_b/area/mc129-1.jpg

Answer 1

The shaded region is two halves of a circle with diameter equal to the edge length of the square. The probability of selecting a point in the shaded area is just the area of that circle / the area of the square. You don't actually need to know the edge length to figure out that ratio...

Answer 2

@whpalmer4 it says that A point in the figure is selected at random. Find the probability that the point will be in the shaded region.

Answer 3

Yes, and what I described is how you would do that. The probability is simply the ratio of the area of interest to the area of the square.

The area of the circle (which has been cut in half and the sides swapped around, which does not alter the area) is given by
\[A_c = \pi r^2\]

The area of the square (which has sides that are twice the radius of the circle in length) is given by
\[A_s = (2r)^2 = 4r^2\]

The probability of a randomly chosen point being in the shaded area is
\[\frac{A_c}{A_s} =\]

Answer 4

You'll see that the final result does not depend on the dimensions of the square or circular regions...