Question

A point is chosen at a random in the square shown below. Find the probability that the point is in the shaded circular region. each side of the square is 12cm, and the radius of the circle is 6cm.

Answer 1

At random, the probability of falling into a region is proportional to the area of the region.
Area of circle = pi*(r^2)=36 pi
Area of square = 12*12 = 144
Therefore probability of falling into circle
P(circle) = area of circle / area of square
=36pi/144
=pi/4
=0.785 approximately