Consider the experiment of throwing a dart at a circular dartboard of radius 1. Assume that in the experiment, the dart always hits the board, and the probability of the dart hitting a given region is proportional to the area of that region.
(a) Find a mathematical description for the sample space in this experiment.
(b) Find a formula for the probability of the dart hitting a given region.
(c) Suppose that the bull's eye is a disk of radius 0.05 . Find the probability of getting a bull's eye.
(d) Find the probability of hitting a particular point (x,y) on the dartboard.
The probability of hitting the bull's eye is clearly demonstrated in this solution.