# Simple symmetric random walk hitting a level within finite steps

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?

• Dec 10, 2019 at 6:50