Explaining the Bayes' theorem graphically

The Bayes’ theorem on conditional probabilities is normally presented to students in introductory courses/modules on Statistics and Probability. This because most STEM students will make use of conditional probabilities in their professional lives with or without noticing. However, maybe because of the unfamiliar notation or because of the variety of ways in which this theorem can be formulated, most students have trouble understanding it. Moreover, when it comes to practical applications and problem exercises, most students (who have generally memorised its manifold ways of rearranging the conditional probabilities formula along with a few applications) struggle even more to come up with correct solutions. By means of a completely graphical approach, this paper presents an alternative way of explaining the Bayes’ theorem to STEM students. By means of diagrams and schematics the students can see the conditional probabilities represented as areas in a square. Simple geometric operations with these areas (additions and multiplications mostly) allow them, not just to understand this theorem far quicker, but to apply it confidently in almost any possible problem configuration. Overall, this paper offers an alternative or complementary way of explaining this important theorem more clearly to students that take probability courses by conveying it graphically instead of with the traditional mathematical formulae. Through a representative case study, this paper deals provides first-hand evidence about how confusing to understand the Bayes’ theorem might be at first even in simple problems, and how the understanding of this theorem is dramatically improved when presenting it graphically.