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There are $n$ random chords drawn in a circle. I am trying to determine the expected number of points in which the chords intersect within the circle.

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    You need to specify the distribution the random chords are chosen with. There are several intutively "reasonable" distributions on the chords in a circle that give different answers; see [Bertrand's paradox](http://en.wikipedia.org/wiki/Bertrand_paradox_%28probability%29).2011-10-16

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