We present fully polynomial-time randomised approximation schemes (FPRAS) for the two-terminal reliability problem on general graphs, both directed and undirected. For directed graphs with $n$ vertices and $m$ arcs, the running time is $\widetilde{O}(nm\varepsilon^{-2})$, where $\varepsilon$ is the relative error. For undirected graphs with $n$ vertices and $m$ edges, it runs in $\widetilde{O}(m+n^2\varepsilon^{-2})$. We also show that the complementary unreliability problem is #BIS-hard.

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