Let $G=(V,E)$ be an undirected graph and $p \colon E \mapsto (0,1]$ defines weights of its edges.

Let's fix two connected vertices $v_1, v_2 \in V$.

Random graph $G'=(V,E')$ is obtained from $G$ by removing each edge $e \in E$ with probability $1-p(e)$.

What is the probability that connectivity between $v_1$ and $v_2$ is preserved in $G'$?