Paternity testing 3: exclusion probabilities

Blood typing with several blood systems is used in many countries to determine paternity or nonpaternity with respect to an alleged father. Various probabilities are usually presented, in particular: the conditional probability of excluding a random man as father given a particular mother-child phenotype combination, and the expected (unconditional) exclusion probability for all mother-child combinations can be calculated for a given blood system. Because these probabilities are of general interest in paternity studies, explicit formulae for the unconditional probabilities have been derived for some of the systems. Algorithms suitable for a microcomputer are given here for finding the exclusion probabilities for any system. These algorithms avoid the need for developing new formulae whenever a new system is introduced or a current system is extended through the addition of further alleles.