Start here · Essential guide
Bayes Theorem Explained with Everyday Examples
Derive Bayes theorem from conditional probability and see it work on a frequency tree with an everyday spam-filter example, step by step and with checked numbers.
Methods and Tools
Conditional Probability and Bayes
Updating chances when new information arrives.
Base Rate Neglect and Why It Misleads
Base rate neglect means ignoring how common something is. See how it turns an accurate-seeming detector into a mostly wrong one, with checked illustrative numbers.
False Positives in Screening Tests
Why a positive result from an accurate screening test can still be more likely wrong than right, shown with illustrative frequencies and checked arithmetic.
Independent Versus Dependent Events
Learn the difference between independent and dependent events by comparing draws with and without replacement, with checked card and marble examples.
Natural Frequencies: An Easier Way to Think About Risk
Why counts out of 1,000 are easier to reason with than percentages, with a checked step-by-step conversion of a screening-style problem into plain counts.
Probability Trees for Multi-Step Events
Learn to draw probability trees that track conditional chances step by step, with a checked two-draw example and clear rules for multiplying and adding branches.
Reading Hidden Information in Card Games with Bayes
How observed plays and visible cards update the likely holdings of other players, explained in general terms with checked illustrative numbers and clear limits.
The Law of Total Probability
Learn how the law of total probability combines cases into one overall chance, and why it is the denominator in Bayes theorem, with a checked illustrative example.
The Prosecutors Fallacy
The prosecutors fallacy confuses the chance of evidence given innocence with the chance of innocence given evidence. See the difference with checked illustrative counts.
Updating Beliefs About a Possibly Biased Coin
Walk through belief updating on coin tosses with simple illustrative priors, comparing a fair coin and a heads-biased coin, with every figure checked.
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