1.12 Probability foundations and Bayes
You can update a belief correctly when new evidence arrives.
Before:00. Orientation & SetupUnlocks:03. Data Handling & Analysis04. Classical AI — Agents, Search & Knowledge Representation
Conditional probability and Bayes' theorem are the grammar of reasoning under uncertainty, anchoring everything from spam filters to model evaluation. The medical-test example carries the single most important lesson in the subject: base rates dominate, and ignoring them produces confidently wrong answers. It opens the probability sequence because every later distribution and estimator speaks this language. The classic confusion is reading the probability of the evidence given the disease as the probability of the disease given the evidence — they differ enormously, and Bayes is the bridge.
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Sample spaces, events, axioms
The formal skeleton of probability: what can happen, what counts as an event, and the three rules everything else is derived from. Short, and worth doing properly once.
Conditional probability and independence
The probability of something given that something else is known, and the special case where knowing makes no difference. Independence is assumed far more often than it is checked.
Introduction to Probability & Statistics (18.05) · CourseBayes' theorem and the base-rate trap
The rule for updating a belief when evidence arrives, and the trap of ignoring how rare something was to begin with. That trap is behind a great many confidently wrong conclusions.
Worked medical-test and spam-filter examples
Two worked examples where the intuitive answer is badly wrong and the calculation is short. These are the examples worth being able to reproduce from memory.
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