Question

A circle is inscribed in a square. A point in the figure is selected at random. Find the probability that the point will be in the shaded region.

A.ABOUT 67%
B.ABOUT 95%
C.ABOUT 75%
D.ABOUT 80%

Answer 1

80%

Explanation:

Answer 2

P of selecting point on the shaded region = shaded area/whole area
P( selecting point on the shaded ) = ( the four shaded circles ) / the whole square
P of selecting point on the shaded = ( 4 * ( π * r^2 ) )/ x^2
P of selecting point on the shaded = ( 4 * ( π * (x/4)^2 ) )/ x^2
P of selecting point on the shaded = ( 4 * ( π * x^2/16 ) )/ x^2
P of selecting point on the shaded = ( π * x^2/4 )/ x^2
P of selecting point on the shaded = x^2( π/4 )/ x^2
P( selecting point on the shaded ) = π/4 ≈ 0.7854 ≈ 79%
=80%
D is right option hope this helps