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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?

See The Solution Submitted by DJ    
Rating: 4.4667 (15 votes)

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re: My idea as well | Comment 8 of 21 |
(In reply to My idea as well by Gamer)

If the first point happens to be 0 degrees (or define 0 degrees as where the first point falls), and the second at say 30 degrees, then the third has to be between 0 and 180 or between 0 and -150. The only way for the test to fail if the first two were as stated would be for the third point to be between -150 and -180 (that is between 180 and 210, the same thing). So that particular case is not 1/2, but 30/360 = 1/12 of failing, or 11/12 of passing.
  Posted by Charlie on 2003-05-19 15:44:21

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