False positives and false negatives exist in a trade-off balance. In almost any real-world situation the price for decreasing one is increasing the other. For instance the criminal justice system is not perfect. It allows some guilty people to go free (false negatives), and convicts some innocent people (false positives).
Poll The trade-off between false positives and false negatives Assume that the false positives and false negatives are uniformly distributed over the full range of crimes, from the least serious to the most serious. You'd think that the most serious crimes would have a very low false positive rate (innocent people convicted), but as
The Innocence Project and others have shown, this is far from true. Personally I think the most serious crimes also create a powerful desire to punish *somebody*, even if they're innocent, just to give the illusion of justice.