27. Consider a disk centered at O with radius R. Suppose that n ≥ 3 points P1, P2, ... , Pn are independently placed at random inside the disk. Find the probability that all these points are contained in a closed semicircular disk. Hint: For each 1 ≤ i ≤ n, let Ai be the endpoint of the radius through Pi and let Bi be the corresponding antipodal point. Let Di be the closed semicircular disk OAiBi with negatively (clockwise) oriented boundary. Note that there is at most one Di, 1 ≤ i ≤ n, that contains all the Pi’s.