Issues examined in the chain of reasoning are whether a reported match is a true match, whether the suspect is the source of the trace, and whether the suspect is the perpetrator of the crime. Part I of the article examines the first issue and discusses ways of defining and estimating the false positive error rates at DNA laboratories. Parts II and III address the second and third issues, respectively. These sections introduce the "source probability error" and "ultimate issue error" and show how experts often commit these errors at trial with assistance from attorneys on both sides. Part IV introduces two related exaggerations, the "P(another match) error" and the "numerical conversion error." Part V provides a simple and general explanation for the persistence of the errors identified. Part VI concludes with a discussion of the ways in which scientists can take advantage of their roles as teachers, expert witnesses, and researchers to educate the courts about the meaning and limits of probabilistic DNA evidence. 66 footnotes