The DNA profiles of two individuals can have 0, 1, or 2 pairs of alleles that are the same at each locus. These events may be called mismatches, partial matches or matches, respectively, and they have probabilities that depend on the population proportions of alleles as well as the population structure parameter theta. The observed and expected numbers of pairs of individuals with various numbers of matching or partially matching loci in FBI and Australian databases are found to be in good agreement provided theta is set equal to some small value greater than zero. The likelihood ratios for two individuals having a specified degree of relationship versus being unrelated also depend on the numbers of matching and partially matching loci, but even unrelated pairs of individuals can have likelihood ratios that support hypotheses of relatedness. Matching probabilities allow predictions to be made for the sizes of databases that are expected to contain a pair of individuals with high numbers of matching loci. It is very likely that two individuals with at least 9 matching loci among the 13 CODIS loci have already been typed.