Perhaps, conditioned by the "99%" we see plastered across the face of home pregnancy tests, we are given the impression that the paternity testing labs will achieve an accurate result in only 99.9% of paternity cases. Actually, this is not quite the way to understand the benchmark that all DNA labs strive to achieve.
One way to understand this measure more accurately is to think of a lottery. While the chances that any one person will have chosen the winning six numbers are exceedingly remote, occasionally more than one winner emerges. Since a person’s genetic makeup is unique, the odds are overwhelmingly against any specific two unrelated people sharing a complete DNA profile. However, in paternity testing, since only a limited number of genetic markers are tested, it is possible that across a large population, two people have, just by random chance, enough genes in common to produce a false positive report. In order to compensate for this statistical fact, the paternity testing labs generally test a large enough number of genetic marker systems so that the theoretical possibility of a second person also being included is generally very small.
Even when a child’s DNA and the alleged father’s DNA are an exact match, there will always be a theoretical possibility that someone else fathered the child. But in order for that to be the case, someone else with similar genetic markers (a rarity in itself) had to have a sexual relationship with the mother. Once we determine a probability of paternity to such a high degree, the likelihood that someone other than the alleged father is indeed the biological father is so small that most courts tend to disregard that possibility, and in the absence of evidence to the contrary, consider the test reliable proof of paternity.
So when you read a lab report stating that John Doe "cannot be excluded" as the father of John Doe Jr. with probability of paternity reaching 99.9%, rest assured that these results are 100% accurate.