# Line through a Square

A unit square is drawn in the Cartesian plane with vertices at $$(0,0),(0,1),(1,0),(1,1)$$. Two points $$P,Q$$ are chosen uniformly at random, $$P$$ from the boundary of the square and $$Q$$ from the interior of the square. The line $$L_1$$ through P and Q is drawn. The probability that the points $$(0,0) \mbox{ and } (1,1)$$ are both on the same side of $$L_1$$ 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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