# Line through a Square

**Discrete Mathematics**Level 4

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 \(a + b\)?

**Your answer seems reasonable.**Find out if you're right!

**That seems reasonable.**Find out if you're right!

Already have an account? Log in here.