This paper proposes a resampling simulator that will calculate probabilities of detecting invasive species infesting hosts that occur in large numbers. Different methods were examined to determine the bias of observed cumulative distribution functions (c.d.f.s), generated from prototype resampling simulators. One involved seeing if they matched theoretical c.d.f.s, which were generated using formulae for calculating the probability of the union of many events (union formulae), which are known to be correct. Others involved assessing the bias of observed c.d.f.s, generated from using prototype resampling simulators operating on much larger simulated populations, when computation of theoretical c.d.f.s from the union formulae was not practical. Examples are given for using the proposed resampling simulator for detecting an invasive insect pest within the context of an invasive species management system.