A point P is randomly selected from the square region with vertices at $(\pm 1, \pm 1)$. What is the probability that P is within one unit of the origin? Express your answer as a common fraction in terms of pi.
Area of the square = 2 x 2 = 4 units2
Area within 1 unit of origin is a circle with radius 1 area = pi 1^2
pi / 4