On Feb. 5, 1987, Vilma Ponce and her infant daughter were stabbed to death in their Bronx, N.Y., apartment. Police arrested a suspect, Joseph Castro, on whose wristwat they found a small bloodstain. The police took the evidence to Lifecodes Corp. in Valhalla, N.Y., where lab analysis convinced the company’s scientists that DNA retrieved from the blood on the watchface matched that of the dead woman. If true, this would have put Castro at the scene of the crime. Chances of the match being coincidental were 100 million to one, Lifecodes scientists later testified.

But late last summer, two and a half years after Castro’s arrest, a New York State Supreme Court judge, Gerald Scheindlin. ruled that those odds were not good enough to convict the suspect. Indeed, the judge ruled in a pretrial hearing, Lifecodes’ DNA test results were not even reliable enough to be used as evidence against...

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