Common Fallacies of Probability in Medical Context: A Simple Mathematical Exposition

This paper presents and explores the most frequent and most significant fallacies about probability in the medical fields. We allude to simple mathematical representations and derivations as well as to demonstrative calculations to expose these fallacies, and to suggest possible remedies for them. We pay a special attention to the evaluation of the posterior probability of disease given a positive test. Besides exposing fallacies that jeopardize such an evaluation, we offer an approximate method to achieve it under justified typical assumptions, and we present an exact method for it via the normalized two-by-two contingency matrix. Our tutorial exposition herein might hopefully be helpful for our intended audience in the medical community to avoid the detrimental effects of probabilistic fallacies. As an offshoot, the pedagogical nature of the paper might allow probability educators to utilize it in helping their students to learn by unraveling their private misconceptions about probability.