We present a method for reasoning about fault-tolerance in unbounded robotic swarms. We introduce a novel semantics that accounts for the probabilistic nature of both the swarm and possible malfunctions, as well as the unbounded nature of swarms systems. We define and interpret a variant of probabilistic linear-time temporal logic on the resulting executions, including those resulting from faulty behaviour by some of the agents in the swarm. We introduce the decision problem of parameterised fault-tolerance, which concerns determining whether a probabilistic specification holds under possibly faulty behaviour. We introduce a procedure that we implement and use to study a foraging protocol from swarm robotics, and report the experimental results obtained.