In quarantine and certification programs, intensive sampling may be needed to determine if lots or shipments of plants, pots, cuttings, or other units are free of plant-parasitic nematodes and other plant pests. It is essential for each quarantine program to define an acceptable tolerance limit for each pest sampled, recognizing that zero tolerance requires sampling everything in the shipment, which is usually impractical. The binomial and hypergeometric probability distributions were used as bases for determining probabilities of detecting various infestation levels as increasing numbers of samples are collected. Probabilities of detecting infestations of 50%, 10%, 5%, 1%, or 1 unit in lot sizes of 100, 1 000, 10 000, and 100 000 units are provided for selected numbers of samples. According to the binomial probability distribution, if 5% of the units in a lot are infested, 59 and 90 samples, respectively, would be required to detect the infestation 95% and 99% of the time. When only
