Another misuse of statistics: Many people expect that FBI uses the DNA database in the following way:
1. get DNA sample from the crime scene
2. match DNA sample against all samples in the database
3. if you got a match, you got the killer.
This is not how it works. Say the real odds of a false positive are ten million to one. In a country of say 300 million people this still gives an expected 30 people who match the sample from the scene. Is each of them the criminal? Clearly not.
How it really works? Imagine that you already identified several suspects. If you take DNA samples of these few people and one of them matches the DNA from the hair from the scene, you can still conclude that given your knowledge, with a very high probability the person in question was present at the crime scene.
In other words, using DNA tests is perfectly reasonable as long as you know what you are doing, even if the probability of a false positive is several orders of magnitude larger than one to a billion.