Abstract
Estimation of numbers of organisms is often made using dilution series, for example when examining water samples for coliform organisms. In this paper the most probable numbers (MPNs) are calculated for a 15-tube series consisting of five replicates at three consecutive tenfold dilutions. Exact conditional probabilities are computed to replace previous approximations. When growth is observed in several of the tubes it is not realistic to select a single MPN. Instead a most probable range (MPR) should be reported. But using an MPR creates problems when comparison has to be made with a legislated, single-valued Standard. It is suggested that the wording of the Standards should be expressed differently when the multiple tube method is used.