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March 25, 2017

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Two points are chosen uniformly at random on the unit circle and joined to make a chord C_1. This process is repeated 3 more times to get chords C_2, C_3, C_4. The probability that no pair of chords intersect can be expressed as \frac{a}{b} where a and b are coprime positive integers. What is the value of a + b?

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