An expansion is derived for the cumulative probability P, that is, the sum of the first p terms of a series of hypergeometrio probabilities. If a batch of N has a proportion defective x, P can be Been as the probability that less than p defectives will be found in a sample of n. The expansion is in descending powers of squares of N −1/2n +1/2, as is the series for the inverse, i.e. P given, x unknown; the first two terms of both are obtained. Each is illustrated by a practical example in which several values obtained from the first term alone and from the Bum of the firet two terms are compared with exact values; the approximations seem more than sufficient for sampling problems except for probabilities extremely near 0 or 1, and are also simple to calculate.