Solution
= Solution
A closed circuit surrounding the origin and passing through $(m,0)$ has diameter at least $m$. By the one-point estimate used in part (b2), its probability is at most $Ce^{-cm}$. Therefore
$$
\mathbb P(\exists m\geq n\text{ on such a circuit})
\leq\sum_{m\geq n}Ce^{-cm}
\leq C'e^{-c'n}.
$$