Methods for non-invasive prenatal paternity testing are disclosed herein. The method uses genetic measurements made on plasma taken from a pregnant mother, along with genetic measurements of the alleged father, and genetic measurements of the mother, to determine whether or not the alleged father is the biological father of the fetus. This is accomplished by way of an informatics based method that can compare the genetic fingerprint of the fetal DNA found in maternal plasma to the genetic fingerprint of the alleged father.