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The most probable number method, otherwise known as the method of Poisson zeroes, is a method of getting quantitative data on concentrations of discrete items from positive/negative data.
There are many discrete entities that are easily detected but difficult to count. Any sort of amplification reaction or catalysis reaction obliterates easy quantification but allows presence to be detected very sensitively. Common examples include microorganism growth, enzyme action, or catalytic chemistry. The MPN method involves taking the original solution or sample, and subdividing it by orders of magnitude , and assessing presence/absence in multiple subdivisions.
The degree of dilution at which absence begins to appear indicates that the items have been diluted so much that there are many subsamples in which none appear. A suite of replicates at any given concentration allow finer resolution, to use the number of positive and negative samples to estimate the original concentration within the appropriate order of magnitude.
In microbiology, the cultures are incubated and assessed by eye, bypassing tedious colony counting or expensive and tedious microscopic counts. Presumptive, confirmative and completed tests are a part of MPN.