Just a few chords, please...

Consider 3 random chords drawn in a circle. (Note that the random chords are established using the 'random endpoints' method, i.e., the endpoints of any chord are two randomly chosen points on the circumference of the circle.)

Now let \(p(k)\) represent the probability that there will be a total of \(k\) points of intersection involving these 3 random chords, with \(0 \le k \le 3\). (Note that if more than 2 chords intersect at the same point then that counts as just one point of intersection.)

Then if \(p(0) - p(1) + p(2) - p(3) = \dfrac{a}{b}\), where \(a\) and \(b\) are positive coprime integers, find \(a + b\).

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