A method of estimating the fraction of fetal DNA in DNA obtained from a bodily fluid of a pregnant individual, the method comprising: (a) aligning or otherwise mapping DNA segment sequences derived from sequencing the DNA in the bodily fluid to one or more designated polymorphisms on a reference sequence, wherein the aligning or otherwise mapping is performed using a computational apparatus programmed to map nucleic acid sequences to the one or more designated polymorphisms; (b) determining allele frequencies of the mapped DNA segment sequences for at least one of the designated polymorphisms; (c) classifying the at least one designated polymorphism based on a combination of the zygosity of the pregnant individual and the zygosity of the fetus; and (d) estimating the fraction of fetal DNA in the DNA obtained from the pregnant individual using the allele frequencies determined in (b) in conjunction with the classification of zygosities from (c), wherein (b)-(d) are performed on one or more processors running under program instructions for the determining, classifying and estimating; and wherein the classifying in (c) classifies the at least one designated polymorphism into one of the following combinations: (i) the pregnant individual is homozygous and the fetus is homozygous, (ii) the pregnant individual is homozygous and the fetus is heterozygous, (iii) the pregnant individual is heterozygous and the fetus is homozygous, and (iv) the pregnant individual is heterozygous and the fetus is heterozygous. (a) aligning or otherwise mapping DNA segment sequences derived from sequencing the DNA in the bodily fluid to one or more designated polymorphisms on a reference sequence, wherein the aligning or otherwise mapping is performed using a computational apparatus programmed to map nucleic acid sequences to the one or more designated polymorphisms; (b) determining allele frequencies of the mapped DNA segment sequences for at least one of the designated polymorphisms; (c) classifying the at least one designated polymorphism based on a combination of the zygosity of the pregnant individual and the zygosity of the fetus; and (d) estimating the fraction of fetal DNA in the DNA obtained from the pregnant individual using the allele frequencies determined in (b) in conjunction with the classification of zygosities from (c), wherein (b)-(d) are performed on one or more processors running under program instructions for the determining, classifying and estimating; and wherein the classifying in (c) classifies the at least one designated polymorphism into one of the following combinations: (i) the pregnant individual is homozygous and the fetus is homozygous, (ii) the pregnant individual is homozygous and the fetus is heterozygous, (iii) the pregnant individual is heterozygous and the fetus is homozygous, and (iv) the pregnant individual is heterozygous and the fetus is heterozygous. wherein (b)-(d) are performed on one or more processors running under program instructions for the determining, classifying and estimating; and wherein the classifying in (c) classifies the at least one designated polymorphism into one of the following combinations: (i) the pregnant individual is homozygous and the fetus is homozygous, (ii) the pregnant individual is homozygous and the fetus is heterozygous, (iii) the pregnant individual is heterozygous and the fetus is homozygous, and (iv) the pregnant individual is heterozygous and the fetus is heterozygous.