A method for determining a ploidy status of a chromosome in a gestating fetus wherein the method is executed for a plurality of gestating fetuses, the method comprising: processing a first sample that contains DNA from the mother of the fetus and DNA from the fetus by purifying the DNA to obtain a second sample; determining the percent of DNA that is fetal in the second sample; measuring the DNA in the second sample by sequencing a set of polymorphic alleles on the chromosome; calculating, on a computer, allele ratios at the set of polymorphic alleles from the DNA measurements made on the second sample; creating, on a computer, a plurality of ploidy hypotheses concerning expected allele ratios at the set of polymorphic alleles on the chromosome for different possible ploidy states of the chromosome; building, on a computer, a joint distribution model for heterozygosity rates of each polymorphic allele on the chromosome for each ploidy hypothesis using the DNA measurements made on the second sample; determining, on a computer, a relative probability of each of the ploidy hypotheses using the joint distribution model and the allele ratios calculated for the second sample, taking into account the fraction of fetal DNA in the samples, wherein for an individual SNP i, the log likelihood of hypothesis H is defined as: LIK i, H = log lik x i | m i, f i, H, cf = ∑ c p c | m i, H * log lik x i | m i, c, H, cf where p c | m i, H = ∑ f p c | m i, f, H * p f | p A i where x i is P(A|i,S), which is the probability of having a given allele A on SNP i, given the sequence measurements S; and m i is the mother genotype; and cf is the determined fetal fraction; and pA i is the population frequency of A allele on this SNP; and calling the ploidy state of the fetus by selecting the ploidy state corresponding to the hypothesis with the greatest probability, thereby determining the ploidy status of a chromosome in a gestating fetus; wherein the first sample has been isolated from maternal blood; wherein processing the first sample further comprises amplifying the DNA; wherein the set of polymorphic alleles are SNPs. processing a first sample that contains DNA from the mother of the fetus and DNA from the fetus by purifying the DNA to obtain a second sample; determining the percent of DNA that is fetal in the second sample; measuring the DNA in the second sample by sequencing a set of polymorphic alleles on the chromosome; calculating, on a computer, allele ratios at the set of polymorphic alleles from the DNA measurements made on the second sample; creating, on a computer, a plurality of ploidy hypotheses concerning expected allele ratios at the set of polymorphic alleles on the chromosome for different possible ploidy states of the chromosome; building, on a computer, a joint distribution model for heterozygosity rates of each polymorphic allele on the chromosome for each ploidy hypothesis using the DNA measurements made on the second sample; determining, on a computer, a relative probability of each of the ploidy hypotheses using the joint distribution model and the allele ratios calculated for the second sample, taking into account the fraction of fetal DNA in the samples, wherein for an individual SNP i, the log likelihood of hypothesis H is defined as: LIK i, H = log lik x i | m i, f i, H, cf = ∑ c p c | m i, H * log lik x i | m i, c, H, cf where p c | m i, H = ∑ f p c | m i, f, H * p f | p A i where x i is P(A|i,S), which is the probability of having a given allele A on SNP i, given the sequence measurements S; and m i is the mother genotype; and cf is the determined fetal fraction; and pA i is the population frequency of A allele on this SNP; and calling the ploidy state of the fetus by selecting the ploidy state corresponding to the hypothesis with the greatest probability, thereby determining the ploidy status of a chromosome in a gestating fetus; wherein the first sample has been isolated from maternal blood; wherein processing the first sample further comprises amplifying the DNA; wherein the set of polymorphic alleles are SNPs. x i is P(A|i,S), which is the probability of having a given allele A on SNP i, given the sequence measurements S; and m i is the mother genotype; and cf is the determined fetal fraction; and pA i is the population frequency of A allele on this SNP; and calling the ploidy state of the fetus by selecting the ploidy state corresponding to the hypothesis with the greatest probability, thereby determining the ploidy status of a chromosome in a gestating fetus; wherein the first sample has been isolated from maternal blood; wherein processing the first sample further comprises amplifying the DNA; wherein the set of polymorphic alleles are SNPs.