 This analysis portrays the prosecutor’s case as weaker than it need be. If the investigators narrowed down the set of suspects to, say, 100 people—a potential piece of information the defense ignored—the match would make the defendant 16% likely to be the source. This fact can be verified using Bayes’ theorem (left as an exercise for the reader). Even assuming, as the defense claims, that the pool of suspects comprises as many as 10,000 people, the prior probability that the defendant is the source would be \(\slashfrac{1}{10,000}\), and since the defendant matches the traces, this probability should rise to (approximately) \(\slashfrac{1}{500}\). Given the upward shift in the probability from \(\slashfrac{1}{10,000}\) to \(\slashfrac{1}{500}\), the match should not be considered worthless evidence (more on this later in  §2.1).