Methods, software, and systems are provided for determining the probability of an overlap set of entities having an overlap size, where the overlap set is independently selected from two sets of non-identical entities. Applications of the invention to microarrays are provided. Probability distributions are provided for determining the probability that the size of an overlap gene set from two different microarrays occurs by chance. Microarray analysis for determining the size of a statistically significant overlap gene set given two different microarrays is described. Overlap set size probability determinations that account for the total number of genes in two different microarrays and not just the common genes are described.