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

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