# Line through a Square

Probability Level 5

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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