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 Don't Be a Square (Posted on 2003-05-19)
Given n points drawn randomly on the circumference of a circle, what is the probability they will all be within any common semicircle?

 Submitted by DJ Rating: 4.4667 (15 votes) Solution: (Hide) For n points choose any given point and evaluate the probability that the other n-1 lie within a semicircle going clockwise. This probability is (1/2)^(n-1). Given that there are n points to start with the overall probability is n/2^(n-1).This may seem like an abuse of taking the sum of probabilities, but in this situation there are only two cases (only zero or one of the events may be true), which eliminates the problem of joint probabilities.

 Subject Author Date The Solution & Generalization Charlie 2003-05-24 06:01:53 Web Research Charlie 2003-05-23 03:51:22 re(5): Simulation DJ 2003-05-22 11:57:25 re(4): Simulation Charlie 2003-05-22 05:25:35 re(3): Simulation DJ 2003-05-21 19:23:55 re(2): Simulation Charlie 2003-05-21 03:40:30 re: Simulation Charlie 2003-05-20 10:07:34 Simulation Charlie 2003-05-20 10:03:08 re(3): Solution Bryan 2003-05-20 06:26:38 re: Am I correct in saying this Charlie 2003-05-20 04:53:19 Am I correct in saying this sendil 2003-05-20 01:06:32 re: Numerical Answers Charlie 2003-05-19 17:59:22 re(2): Solution Charlie 2003-05-19 16:15:15 re: My idea as well Charlie 2003-05-19 15:44:21 re(3): Numerical Answers Charlie 2003-05-19 15:40:22 re: Solution Bryan 2003-05-19 12:52:22 My idea as well Gamer 2003-05-19 12:10:27 Solution Bryan 2003-05-19 10:14:41 re(2): Numerical Answers Gamer 2003-05-19 10:11:34 re: Numerical Answers Charlie 2003-05-19 09:43:33 Numerical Answers Charlie 2003-05-19 09:40:39

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