16. Suppose that n points are independently chosen at random on the perimeter of a circle, and we want the probability that they all lie in some semicircle.

(That is, we want the probability that there is a line passing through of the circle such that all the points are on one side of that line.)

Let $P_1,..., P_n$ denote the n points. Let A denote the event that all are contained in some semicircle, and let $A_i$ be the event that all lie in the semicircle beginning at the point $P_i$, and going clockwise i = 1,..., n.

(a) Express A in terms of the $A_i$.

(b) Are the $A_i$ mutually exclusive?

(e) Find P(A).