An ex vivo method for establishing whether an alleged father is the biological father of a fetus that is gestating in a pregnant mother, the method comprising: making genotypic measurements of single nucleotide polymorphism alleles, at a plurality of polymorphic loci, on genetic material obtained from the alleged father, genetic material obtained from the pregnant mother and on a mixed sample of DNA originating from a blood sample obtained from the pregnant mother, where the mixed sample of DNA comprises fetal DNA and maternal DNA; wherein said genotypic measurements are output measurements from a genotyping platform comprising the identity of the plurality of nucleotides at the plurality of polymorphic loci; determining, on a computer, the probability that the alleged father is the biological father of the fetus gestating in the pregnant mother by obtaining population frequencies of alleles for each locus in the plurality of polymorphic loci; creating a partition of the range of possible fractions of fetal DNA in the mixed sample of DNA, wherein the partition of possible fetal fractions ranges from 2% foetal fraction to 30% fetal fraction, the foetal fraction being determined by making genotypic measurements at a plurality of polymorphic loci from the mixed sample of DNA; obtaining genotypic data at the plurality of polymorphic loci from the alleged father; calculating a probability that the alleged father is the biological father of the fetus using the genotypic measurements made on the genetic material from the alleged father, and the mixed sample of DNA; for each of the possible fetal fractions in the partition using a maximum likelihood estimation, or a maximum a posteriori technique; and determining the probability that the alleged father is the biological father of the fetus by combining the calculated probabilities that the alleged father is the biological father of the fetus for each of the possible fetal fractions in the partition; calculating a probability that the alleged father is not the biological father of the fetus given the genotypic measurements made from the genetic material from the mother, the alleged father and the mixed sample of DNA, and the given obtained allele population frequencies; for each of the possible foetal fractions in the partition; and determining the probability that the alleged father is not the biological father of the fetus by combining the calculated probabilities that the alleged father is not the biological father of the fetus for each of the possible fetal fractions in the partition; and establishing whether the alleged father is the biological father of the fetus using a single hypothesis rejection test, a maximum likelihood estimation, or a maximum a posteriori technique given the determined probability that the alleged father is the biological father of the fetus. making genotypic measurements of single nucleotide polymorphism alleles, at a plurality of polymorphic loci, on genetic material obtained from the alleged father, genetic material obtained from the pregnant mother and on a mixed sample of DNA originating from a blood sample obtained from the pregnant mother, where the mixed sample of DNA comprises fetal DNA and maternal DNA; wherein said genotypic measurements are output measurements from a genotyping platform comprising the identity of the plurality of nucleotides at the plurality of polymorphic loci; determining, on a computer, the probability that the alleged father is the biological father of the fetus gestating in the pregnant mother by obtaining population frequencies of alleles for each locus in the plurality of polymorphic loci; creating a partition of the range of possible fractions of fetal DNA in the mixed sample of DNA, wherein the partition of possible fetal fractions ranges from 2% foetal fraction to 30% fetal fraction, the foetal fraction being determined by making genotypic measurements at a plurality of polymorphic loci from the mixed sample of DNA; obtaining genotypic data at the plurality of polymorphic loci from the alleged father; calculating a probability that the alleged father is the biological father of the fetus using the genotypic measurements made on the genetic material from the alleged father, and the mixed sample of DNA; for each of the possible fetal fractions in the partition using a maximum likelihood estimation, or a maximum a posteriori technique; and determining the probability that the alleged father is the biological father of the fetus by combining the calculated probabilities that the alleged father is the biological father of the fetus for each of the possible fetal fractions in the partition; calculating a probability that the alleged father is not the biological father of the fetus given the genotypic measurements made from the genetic material from the mother, the alleged father and the mixed sample of DNA, and the given obtained allele population frequencies; for each of the possible foetal fractions in the partition; and determining the probability that the alleged father is not the biological father of the fetus by combining the calculated probabilities that the alleged father is not the biological father of the fetus for each of the possible fetal fractions in the partition; and establishing whether the alleged father is the biological father of the fetus using a single hypothesis rejection test, a maximum likelihood estimation, or a maximum a posteriori technique given the determined probability that the alleged father is the biological father of the fetus.