Bayes’ rule trainer
Start with a belief, see the evidence, update your estimate. Each scenario asks you to guess a posterior probability before showing how the answer follows from the cases that match the evidence.
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How to use it
Read the scenario and estimate the probability first. The tool then shows the population of cases and removes those that could not have produced the evidence. Among the cases left, the share that belong to your group is the posterior.
In multi-step scenarios the first answer becomes your new starting belief, and the next observation updates it again. Your score is the average absolute error across every update, so lower is better.
What it teaches
Bayes’ rule weighs how likely the evidence is under each hypothesis by how common each hypothesis was to begin with. The most common mistake, base-rate neglect, is ignoring that second part. It shows up in medical-test puzzles, in interview questions and in reading trading signals.
Key formula
P(A | B) = P(B | A)P(A) / [P(B | A)P(A) + P(B | not A)P(not A)]
Learn the ideas behind it
- Conditional probability, total probability and Bayes’ rule
- Worked examples: probability trees, Monty Hall and Bayesian updating
- Bayesian reasoning