Why do two seemingly unrelated individuals – one black and one white – share the same two markers at nine of the 13 places in the standard DNA profile?
In 2001, the DNA unit of Arizona’s state crime laboratory found 122 such matches in a 65,000-person sized database, some of which even shared markers at 10, 11 or 12 places. So how many of these matches might be found in the 11 million-person US national database? But rather than follow up on these findings, the FBI suppressed them, threatening to cut off access to the national database to any lab that independently conducted their own such studies.
But how can this high number of matches be explained? The answer is that there is a huge difference between a random match or a match in a finite sample. Contrary to what most people expect, it does not take a large number of people to have more than a 50% chance to find at least two people that share the same birthday – it actually only takes 23 (this is called the „Birthday Problem“). However if you randomly pick a person on the street the probability that they would have a particular birthday is much smaller.
So what do this findings mean for cases that are routinely proceeded on the basis of only a nine-locus database match, treated by lawyers and courts alike as conclusive proof of guilt?
In one particular case, a man that matched badly degraded DNA samples collected over 30 years ago at a rape and murder crime scene, was sent to life in prison without parole. The prosecution’s argument was that there was only a 1 in 1.1 million chance that a person picked at random would match the crime scene. Why is this statistic wrong? Because this was not a truly random match. Like for the birthday problem, is was a match among a finite pool of candidates – those within the database. The jury however never heard the defense’s alternative statistic. They never heard about the Arizona matches, that sharing alleles at nine loci is not uncommon or that statistically there should be at least two other people living in the area at the time that also matched the evidence.
Source: The Atlantic