give a simple symmetric random walk, denote $\mathbb P_0(T_1 < \infty)$ the probability that starting at $0$ and the first time reaching level 1 within finite discrete time steps. What is $\mathbb P_0(T_1 < \infty)$?
So can I assume that it hits level $1$ within $n$ steps, then use the hitting time thm to calculate the probability? Or is there another way to this?