An archer shoots an arrow at a circular target of radius 50cm. The arrow pierces the target at a random position (X, Y), measured in centimeters from the center of the disk at position (X, Y) = (0, 0). The "bullseye" is a solid black circle of radius 2cm, at the center of the target. Calculate the probability P[B] of the event that the archer hits the bullseye under each of the following models:
(a) X and Y are iid continuous uniform (-50, 50) random variables.
(b) The PDF fX,Y (x, y) is uniform over the 50cm circular target.
(c) X and Y are iid Gaussian (µ = 0, σ = 10) random variables.