Question 22
In a small pond there are eleven lily pads in a row labeled $0$ through $10.$ A frog is sitting on pad $1.$ When the frog is on pad $N,$ $0 \lt N \lt 10,$ it will jump to pad $N - 1$ with probability $\dfrac{N}{10}$ and to pad $N + 1$ with probability $1 - \dfrac{N}{10}.$ 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 being eaten by the snake?