  Let $\mu > 2$ and $\epsilon > 0$. We show that, if $G$ is a sufficiently
large simple graph of average degree at least $\mu$, and $H$ is a random
spanning subgraph of $G$ formed by including each edge independently with
probability $p \ge \tfrac{1}{\mu-1} + \epsilon$, then $H$ contains a cycle with
probability at least $1 - \epsilon$.
