In a small pond there are seven lily pads in a row labeled $0$ through $6$. A frog is sitting on pad $1$. When the frog is on pad $N$, $0<N<6$, it will jump to pad $N-1$ with probability $\frac{N}{6}$ and to pad $N+1$ with probability $1-\frac{N}{6}$. 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 $6$ it will exit the pond, never to return. What is the probability that the frog will escape without being eaten by the snake?