Question 132
A lattice point is a point whose coordinates are both integers. Suppose Johann walks in a line from the point $(0,2004)$ to a random lattice point in the interior (not on the boundary) of the square with vertices $(0,0)$, $(0,99)$, $(99,99)$, $(99,0)$. What is the probability that his path, including the endpoints, contains an even number of lattice points?