Drunk Man on a Cliff

A drunk man stands 1 step away from the edge of a cliff. At each time step, he takes a step:

• towards the cliff (one step forward) with probability $1/2$;
• away from the cliff (one step backward) with probability $1/2$.

His distance from the edge is modeled by a process $(X_n)_{n\ge 0}$ taking values in $\{0, 1, 2, \dots\}$, with $X_0 = 1$ and $0$ representing falling off.

Question 1: What is the probability that he falls off the cliff?

Question 2: On average, how many steps does he take before falling (given that he falls)?