Suppose n (n>1) points are placed at random on a circumference of a circle. If P(n) denotes the probability that all n points lie on the same side of some diameter - find P(2), P(3) and P(4).

It looks like we already talked about this problem way back in 2003 with the problem Don't Be a Square. The solution was determined to be P(n) = n/2^(n-1)