A method of determining a fractional concentration of fetal DNA in a biological sample taken from a pregnant female with a fetus, the fetus having a father and a mother being the pregnant female, the mother having a maternal genome, the fetus having a fetal genome, wherein the biological sample contains a mixture of maternal and fetal nucleic acids, the method comprising: analyzing a plurality of nucleic acid molecules from the biological sample, wherein analyzing a nucleic acid molecule includes: identifying a location of the nucleic acid molecule in the human genome; and determining a respective allele of the nucleic acid molecule; determining one or more first loci, wherein the fetal genome is heterozygous at each first loci such that the fetal genome has a respective first and second allele at that first loci, and wherein the maternal genome is homozygous at each first loci such that the maternal genome has two of the respective second allele at that first loci, the first allele being different than the second allele, wherein determining a specific locus to be one of the one or more first loci includes: determining a cutoff value for a number of predicted counts of the respective first allele at the specific locus, the cutoff value predicting whether the maternal genome is homozygous and the fetal genome is heterozygous, wherein the cutoff value is determined based on a statistical distribution of numbers of counts for different combinations of homozygosity and heterozygosity at the specific locus; based on the analysis of the plurality of nucleic acid molecules, detecting the respective first allele and the respective second allele at the specific locus; determining a number of actual counts of the respective first allele based on the analysis of the plurality of nucleic acid molecules from the biological sample; and determining the specific locus is one of the first loci when the number of actual counts is less than the cutoff value; for at least one of the first loci: determining a first number P of counts of the respective first allele and a second number Q of counts of the respective second allele; and calculating the fractional concentration based on the first and second numbers. analyzing a plurality of nucleic acid molecules from the biological sample, wherein analyzing a nucleic acid molecule includes: identifying a location of the nucleic acid molecule in the human genome; and determining a respective allele of the nucleic acid molecule; identifying a location of the nucleic acid molecule in the human genome; and determining a respective allele of the nucleic acid molecule; determining one or more first loci, wherein the fetal genome is heterozygous at each first loci such that the fetal genome has a respective first and second allele at that first loci, and wherein the maternal genome is homozygous at each first loci such that the maternal genome has two of the respective second allele at that first loci, the first allele being different than the second allele, wherein determining a specific locus to be one of the one or more first loci includes: determining a cutoff value for a number of predicted counts of the respective first allele at the specific locus, the cutoff value predicting whether the maternal genome is homozygous and the fetal genome is heterozygous, wherein the cutoff value is determined based on a statistical distribution of numbers of counts for different combinations of homozygosity and heterozygosity at the specific locus; based on the analysis of the plurality of nucleic acid molecules, detecting the respective first allele and the respective second allele at the specific locus; determining a number of actual counts of the respective first allele based on the analysis of the plurality of nucleic acid molecules from the biological sample; and determining the specific locus is one of the first loci when the number of actual counts is less than the cutoff value; determining a cutoff value for a number of predicted counts of the respective first allele at the specific locus, the cutoff value predicting whether the maternal genome is homozygous and the fetal genome is heterozygous, wherein the cutoff value is determined based on a statistical distribution of numbers of counts for different combinations of homozygosity and heterozygosity at the specific locus; based on the analysis of the plurality of nucleic acid molecules, detecting the respective first allele and the respective second allele at the specific locus; determining a number of actual counts of the respective first allele based on the analysis of the plurality of nucleic acid molecules from the biological sample; and determining the specific locus is one of the first loci when the number of actual counts is less than the cutoff value; for at least one of the first loci: determining a first number P of counts of the respective first allele and a second number Q of counts of the respective second allele; and calculating the fractional concentration based on the first and second numbers.