Problem 17 Solution

Lets consider the dartboard in polar coordinates. The dart can land at any angle relative to the center with equal probability. Next take the intregral from the least to the greatest distance, 0 to 1. The density function at distance d is 2*pi*d/pi = 2d. So the answer is:

Integral from 0 to 1 of d*2d = 2d³/3 from 0 to 1 = 2/3.

Michael Shackleford, A.S.A.