Non-Intersecting Chords

Probability Level 5

Two points are chosen uniformly at random on the unit circle and joined to make a chord C1C_1. This process is repeated 33 more times to get chords C2,C3,C4C_2, C_3, C_4. The probability that no pair of chords intersect can be expressed as ab\frac{a}{b} where aa and bb are coprime positive integers. What is the value of a+ba + b?

Details and assumptions

A chord of a circle is the line segment between 2 points on the circumference. It does not extend infinitely in either direction.

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