1. A method for determining the presence or absence of fetal aneuploidy from a plasma or serum sample from a pregnant female subject, wherein the sample comprises cell-free nucleic acid molecules from the genome of both the female subject and a fetus, comprising: (a) performing random massively parallel DNA sequencing on at least a portion of the cell-free nucleic acid molecules to generate random sequenced tags; (b) aligning at least a portion of the sequenced tags obtained in step (a) to a reference genome; (c) calculating a fractional representation of a first chromosome from sequenced tags aligned to the first chromosome and sequenced tags aligning to one or more second chromosomes; (d) comparing the fractional representation of the first chromosome to a cutoff value representing the expected fractional representation in the absence of aneuploidy; and (e) based on the comparison step of (d), determining whether fetal aneuploidy is present or absent.