Entanglement distribution by an arbitrarily inept delivery service

We consider the scenario where a company C manufactures in bulk pure entangled pairs of particles, each pair intended for a distinct pair of distant customers. Unfortunately, its delivery service is inept-the probability that any given customer pair receives its intended particles is S is an element of[0,1], and the customers cannot detect whether an error has occurred. Remarkably, no matter how small S is, it is still possible for C to distribute entanglement by starting with nonmaximally entangled pairs. We determine the maximum entanglement distributable for a given S, and also determine the ability of the parties to perform nonlocal tasks with the qubits they receive.