Line through a Square

Probability Level 4

A unit square is drawn in the Cartesian plane with vertices at (0,0),(0,1),(1,0),(1,1)(0,0),(0,1),(1,0),(1,1). Two points P,QP,Q are chosen uniformly at random, PP from the boundary of the square and QQ from the interior of the square. The line L1L_1 through P and Q is drawn. The probability that the points (0,0) and (1,1)(0,0) \mbox{ and } (1,1) are both on the same side of L1L_1 can be expressed as ab\frac{a}{b} where aa and bb are coprime positive integers. What is the value of a+ba + b?

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