Question 11
A token starts at the point $(0, 0)$ of an $xy$-coordinate grid and then makes a sequence of six moves. Each move is $1$ unit in a direction parallel to one of the coordinate axes. Each move is selected randomly from the four possible directions and independently of the other moves. The probability that the token ends at a point on the graph of $|y| = |x|$ is $\frac{m}{n},$ where $m$ and $n$ are relatively prime positive integers. Find $m + n.$