There are a hundred probability courses that hand you formulas to memorize — P(A|B), the bell curve, a table of distributions — and hope you never ask where any of it came from. Don't waste your time there. This one builds every idea from the one thing you already trust: a fair coin. From that single flip we derive counting, then measure, then Bayes, then the entire family of distributions — and we tell you the secret almost no course says out loud: they are not a zoo to memorize, they are one family, each a limit or a case of the last. You'll leave able to re-derive any of it, predict a case you've never seen, and teach it to a friend. Every idea opens with a hook and lands with something you can drag, break, or predict. It's harder than the formula-sheet path. It's worth it — because the person who understands chance from first principles is the one who can actually reason under uncertainty, which is most of real life.
Probability as a counted fraction → combinatorics → the measure on a sample space → the complement.
Start hereLearn something, then flip it — conditioning, total probability, Bayes, and the base-rate trap.
OpenOne atom (Bernoulli), one hub (binomial), and its limits — the normal, Poisson, geometric.
OpenWaiting times, memorylessness, and how to reshape a random variable (the z-map, chi-squared).
OpenJoint structure, expectation and variance, and covariance — how two variables move together.
OpenThe Law of Large Numbers and the Central Limit Theorem — why the bell curve is everywhere.
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