This IB Maths AA AHL Topic 4.13 – Bayes’ Theorem resource develops students’ understanding of how conditional probabilities can be reversed using prior information and new evidence. It begins by introducing Bayes’ theorem as a method for finding P(cause given result) when P(result given cause) is known. Students learn how this process represents Bayesian updating and why it is particularly useful in contexts such as medical testing, diagnosis, quality control, and classification.

The lesson develops confidence in applying Bayes’ theorem to problems involving two or three possible causes. Students use tree diagrams and tables to organise prior probabilities and conditional probabilities, multiply along branches to calculate intersections, and add relevant branches to find the total probability of the evidence. Practice includes disease testing, factory machines, defective products, and selecting counters from different boxes. The resource also connects Bayes’ theorem to independence, showing that evidence produces no probability update when two events are independent. With clear explanations, visual interpretations, worked examples, tree-diagram strategies, exam checklists, and fully worked solutions, this resource helps AHL students build strong conditional probability reasoning in line with IB Mathematics AA expectations.