In a small pond there are eleven lily pads in a row labeled $0$ through $10$. A frog is sitting on pad $2$. When the frog is on pad $N$, $0<N<10$, it will jump to pad $N-1$ with probability $\frac{1}{3}$ and to pad $N+1$ with probability $\frac{2}{3}$. Each jump is independent of the previous jumps. If the frog reaches pad $0$ it will be eaten by a patiently waiting snake. If the frog reaches pad $10$ it will exit the pond, never to return. What is the probability that the frog will escape without being eaten by the snake?