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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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Am I correct in saying this | Comment 11 of 21 |
The first point can be placed anywhere in the circle,the second point as well, the farthest these two can be are on end points of a diameter.We then are in a position to define what is in the same semi-circle and what is not.

It is very clear that the next point onwards there is a 1/2 chance of it falling in the req semi-circle.
So are we looking at (1/2)^n-2 ????????
  Posted by sendil on 2003-05-20 01:06:32
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