Whether a fetus has an aneuploidy associated with a first chromosome is detected using ratios of alleles detected in a maternal sample having a mixture of maternal and fetal DNA. DNA from the sample is enriched for target regions associated with polymorphic loci and then sequenced. Polymorphic loci (e.g., single nucleotide polymorphisms) in the target regions with fetal -specific alleles are identified on a first chromosome and on one or more reference chromosomes. A first ratio of the fetal-specific alleles and shared alleles is determined for the loci on the first chromosome. A second ratioof the fetal-specific alleles and shared alleles is determined for the loci on the reference chromosome(s). A third ratio of the first and second ratio can be compared to a cutoff to determine whetheran aneuploidy is present, and whether die aneuploidy is maternally-derived or paternally-derived.