AMC10 2027 - Self-practice Set 7 Question 7

Eleven lily pads in a row are labeled $0$ through $10$. A frog starts on pad $1$. From pad $N$, where $0\lt N\lt 10$, it jumps to $N-1$ with probability $\dfrac N{10}$ and to $N+1$ with probability $1-\dfrac N{10}$, with each choice depending only on its current position.

At pad $0$ it is eaten; at pad $10$ it escapes permanently. What is its probability of escape?