Suppose that n points are independently chosen at random on the circumference of a circle, and we
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Let P1, . . . ,Pn denote the n points. Let A denote the event that all the points are contained in some semicircle, and let Ai be the event that all the points lie in the semicircle beginning at the point Pi and going clockwise for 180Ë, i = 1, . . . , n.
(a) Express A in terms of the Ai.
(b) Are the Ai mutually exclusive?
(c) Find P(A).
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