An intersection of geometry and combinatorics

Discrete Mathematics Level 4

Consider a square with vertices \((0,0), (0,1), (1,1)\) and \((1,0)\). Choose a random point within the square and draw a line segment from it to \((0,0)\). Next, choose a second random point within the square and draw a line segment from this point to \((1,0)\).

The probability that these two line segments intersect is \(\frac{a}{b}\), where \(a\) and \(b\) are positive coprime integers. Find \(a + b\).

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