There are several famous cases of fallacious statistical arguments leading to wrongful convictions, where recognition of the error was a main major or contributing factor in the eventual overturn of the decision. Such errors are broadly grouped under The Prosecutor's Fallacy - the fallacy of calculating $P(evidence|innocent)$, which is typically tiny, and equating it to $P(innocent|evidence)$, which may not be small when the unconditional probability $P(evidence)$ is itself small.
There are several famous cases of fallacious statistical arguments leading to wrongful convictions, where recognition of the error was a main or contributing factor in the eventual overturn of the decision. Such errors are broadly grouped under The Prosecutor's Fallacy - the fallacy of calculating $P(evidence|innocent)$, which is typically tiny, and equating it to $P(innocent|evidence)$, which may not be small when the unconditional probability $P(evidence)$ is itself small.