Bayes Tree Lab

Bayes Tree Lab turns conditional probability into something you can see, edit, and check. Build a two-stage probability tree, follow every path, and watch Bayes' theorem unfold one line at a time. Then run a seeded simulation and compare what the theory predicts with what actually happens. Every experiment can be saved and reopened later, so you can re-check your work whenever you like. DRAW AND EDIT THE TREE - A clear branch diagram with events A and not-A, then B and not-B. - Edit the prior P(A) and the two conditional probabilities with a slider or by typing. - Sibling branches rebalance automatically, so each pair always adds up to exactly one. - Branch thickness follows probability, so large and small chances are easy to compare. CHECK EVERY PATH - See the joint probability of all four paths, with the multiplication written out. - A built-in check confirms that the paths add up to one. BAYES POSTERIOR, FULLY EXPANDED - Choose whether you observed B or not-B. - Follow three explicit steps: joint probabilities, evidence probability, and the posterior. - Impossible cases, such as an observation with zero probability, are explained instead of hidden. ODDS FORM - See prior odds multiplied by the likelihood ratio to give the posterior odds. - A log-odds axis shows how far the evidence moved your belief. - The result is cross-checked against the standard Bayes posterior. NATURAL FREQUENCIES - View the same problem as head-counts in a population of 100, 1,000, or 10,000. - A plain sentence shows how the posterior comes from simple counting. SEEDED SIMULATION - Enter a random seed and a number of trials, up to one million. - The same seed and inputs always produce the same counts, so results are repeatable. - Compare expected and observed counts for each path, with differences and relative error. - A bar chart and a chi-square test show how well the simulation fits the theory. SAVE, REOPEN, AND VERIFY - Save any run together with its inputs, seed, and counts, plus an optional note. - Reopen it from History at any time. - Tap Re-run to verify to reproduce the run from its seed and confirm every count matches. - Share a plain-text summary of a run with a classmate or teacher. PRACTICE WITH CLASSIC PUZZLES - Guess the answer to well-known base-rate problems such as medical screening, a taxi witness, a spam filter, and factory defects. - Lock in your guess, then see the exact answer, how far off you were, and a simple head-count explanation. - Open any puzzle on the tree to explore it further. - Your best scores are tracked on your device. BUILT FOR LEARNING - Made for students, teachers, and anyone meeting conditional probability for the first time. - Works offline. No account, no sign-in, no ads. - Your data stays on your device. Bayes Tree Lab does not collect any personal information. Questions or feedback? Contact us at [email protected].