In a small pond there are nine lily pads in a row labeled 0 through 8. A frog is sitting on pad 1. When the frog is on pad $N$, $0<N<8$, it will jump to pad $N-1$ with probability $\frac{N}{8}$ and to pad $N+1$ with probability $1-\frac{N}{8}$. 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 8 it will exit the pond, never to return. What is the probability that the frog will escape without being eaten by the snake?