# Non-Intersecting Chords

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 $$a + b$$?

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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