Let $\displaystyle X_1,X_2,...$ be independent identically distributed random variables with $\displaystyle \mathbb{P}(X_1=-1)=\frac{1}{3}, \ \mathbb{P}(X_1=1)=\frac{2}{3}$

Let $\displaystyle Y_0=0$ and set $\displaystyle Y_n=X_1+X_2+...X_n$

By the S.L.L.N's $\displaystyle \frac{Y_n}{n}\rightarrow \frac{1}{3} \; as \ n \rightarrow \infty$

Deduce that with probability 1 the stochastic process {Y_n: n=0,1,2,...} visits the origin at most a finite number of times.

I have no clue where to start with this question could someone please give me a hint

thanks