Surveys of public opinion indicate that people have high expectations for juries. When it comes to serious crimes, most people want errors of convicting the innocent (false positives) or acquitting the guilty (false negatives) to fall well below 10%. Using expected utility theory, Bayes' Theorem, signal detection theory, and empirical evidence from detection studies of medical decision making, eyewitness testimony, and weather forecasting, we argue that the frequency of mistakes probably far exceeds these "tolerable" levels. We are not arguing against the use of juries. Rather, we point out that a closer look at jury decisions reveals a serious gap between what we expect from juries and what probably occurs. When deciding issues of guilt and/or punishing convicted criminals, we as a society should recognize and acknowledge the abundance of error.