The potential for exclusion based on the combination of genetic systems is calculated showing the utility of genetically controlled polymorphic enzyme/protein and immunologic systems. The key to assessing the guilt or innocence in a paternity dispute using genetic evidence is the estimation of the probability of not being excluded by chance alone. This probability is computed under two sets of conditions: a random male supplied the genes in question, or male with a phenotype identical to the accused supplied the genes in question. Contrasting these two probabilities leads to an estimate of the likelihood of guilt or innocence associated with the evidence from blood group genetic systems. The presentation gives two tables for the calculation of these non-exclusion probabilities in paternity disputes for currently used biochemical and immunological systems. The role of Bayes' theorem is discussed in conjunction with these non-exclusion probabilities. (Publisher abstract)