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Don't Be a Square (Posted on 2003-05-19) Difficulty: 4 of 5
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.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
The Solution & GeneralizationCharlie2003-05-24 06:01:53
Web ResearchCharlie2003-05-23 03:51:22
re(5): SimulationDJ2003-05-22 11:57:25
re(4): SimulationCharlie2003-05-22 05:25:35
re(3): SimulationDJ2003-05-21 19:23:55
re(2): SimulationCharlie2003-05-21 03:40:30
re: SimulationCharlie2003-05-20 10:07:34
SimulationCharlie2003-05-20 10:03:08
re(3): SolutionBryan2003-05-20 06:26:38
re: Am I correct in saying thisCharlie2003-05-20 04:53:19
Am I correct in saying thissendil2003-05-20 01:06:32
re: Numerical AnswersCharlie2003-05-19 17:59:22
re(2): SolutionCharlie2003-05-19 16:15:15
re: My idea as wellCharlie2003-05-19 15:44:21
re(3): Numerical AnswersCharlie2003-05-19 15:40:22
re: SolutionBryan2003-05-19 12:52:22
Hints/TipsMy idea as wellGamer2003-05-19 12:10:27
SolutionSolutionBryan2003-05-19 10:14:41
re(2): Numerical AnswersGamer2003-05-19 10:11:34
re: Numerical AnswersCharlie2003-05-19 09:43:33
Some ThoughtsNumerical AnswersCharlie2003-05-19 09:40:39
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