A point P is randomly selected from the square region with vertices at (2,2), (2,0), (0,2), (0,0). What is the probability that P is within one unit of the origin? Express your answer as a common fraction in terms of pi.
See the following :
Note that this boils down to finding the area of the quarter circle with a center at the origin and with a radius of 1 within a square with a side of 2
Area of the quarter circle = pi (1)^2 / 4 = pi/4
Area of the square = 2^2 = 4
Probability = area of quarter circle / area of square = (pi/4) / 4 = pi / 16