Probability theory, especially Bayesian probability, is widely misunderstood by the general public. Lawyers are no different from ordinary members of the public in falling victim to arguments that have been known to mathematicians for decades to be fallacies. The so-called prosecutor’s fallacy and the defendant’s fallacy are two well-known examples that arise from a basic misunderstanding of conditional probability and Bayes’ Theorem. In this paper we introduce what we believe is a previously unreported fallacy, which we refer to as the jury observation fallacy. In this fallacy there is a basic misunderstanding about the belief in probability of guilt when a prior similar conviction by a defendant is revealed after the jury returns a not guilty verdict. Specifically, it is widely believed that the information about the prior conviction might suggest to external observers that the jury verdict was wrong (the belief is that probability of guilt increases). In fact, using very reasonable (and indeed conservative) assumptions it can be shown, using Bayesian reasoning, that such a response is irrational in many situations. To explain the Bayesian argument without exposing readers to any of the mathematical details we
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