Question 5
A moving particle starts at the point $(4, 4)$ and moves until it hits one of the coordinate axes for the first time. When the particle is at the point $(a, b),$ it moves at random to one of the points $(a - 1, b),$ $(a, b - 1),$ or $(a - 1, b - 1),$ each with probability $\frac{1}{3},$ independently of its previous moves. The probability that it will hit the coordinate axes at $(0, 0)$ is $\frac{m}{3^n},$ where $m$ and $n$ are positive integers, and $m$ is not divisible by $3.$ Find $m + n.$