The problem of computing preformability probabilities in stochastic PERT and flow networks is studied when the networks is ﲭinimally designed to withstand any two component failures. Polynomial-time algorithms to compute preformability when the network is planar -- the nonplanar versions being NP-hard -- solve related ﲴwo-path subset problems. Given an acyclic graph with weights on the arcs, the algorithms compute the total weight of all subsets of arcs that are contained in (1) two source-sink paths or (2) two arc-disjoint source-sink paths. A polynomial algorithm is given for (1), and for (2) in the case where the graph is a source-sink planar k-flow graph, that is edge-minimal with respect to supporting k units of flow.