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Four points W, X , Y, Z are chosen at random on the circumference of a circle. What is the probability that WX > YZ?

 Oct 29, 2022
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I am assuming that the four (or n) points are considered in the order that they appear on the circle rather than the order in which they were chosen. (Otherwise, the quadrilateral [polygon] might not be “proper.”) The event “the polygon contains the center of the circle” is equivalent to the event “every diameter of the circle intersects the polygon,” so it is the complement of the event “all n points fall on one side of some diameter of the circle.” PartyCityFeedback Survey

 Oct 29, 2022
edited by Joehollywood  Oct 29, 2022

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