Learn probability in five months
Five months of serious study — 45 minutes a day plus weekend problem sets — gets a learner with calculus comfortable with random variables, joint distributions, conditional expectation, and Bayesian reasoning. About 130 hours total. Enough to stop guessing at probabilistic problems and start solving them.
5 months · ~130 hours · solve real probability problems, think Bayesian
1.Stat 110 — Joe Blitzstein, Harvard
The single best probability course on the internet. Blitzstein lectures with infectious clarity, builds intuition before formalism, and teaches the "story proof" technique that no textbook will. Thirty-four lectures, free on YouTube. Watch them in order, pause to attempt every problem he poses on the board, and don't move on until you can re-derive the previous lecture's main result.
Free
Stat 110 course site →2.Blitzstein & Hwang — Introduction to Probability
The textbook that pairs with Stat 110, written by the same lecturer. Each chapter maps to two or three lectures. The exercises are the point — the strategic-practice problems at the back of each chapter, in particular, are where probability stops being trivia and starts being a way of thinking. Solutions are available online for the odd-numbered ones.
~$80 new, ~$50 used
Stat 110 textbook site →3.MIT 6.041 — Tsitsiklis
If a topic in Blitzstein doesn't click — Markov chains and convergence theorems are common stuck points — go watch the same topic in Tsitsiklis's MIT course. He's drier but more rigorous, and the second exposure from a different angle is what cements understanding. Free on MIT OCW with full problem sets and solutions.
Free
MIT OCW Probability →If this doesn't fit you
If you need probability for machine learning specifically — not as a subject in itself — replace Blitzstein with the relevant chapters of Bishop's Pattern Recognition and Machine Learning. You'll cover less ground but learn exactly what's needed for graphical models and Bayesian inference. Plan on three months and expect gaps in the foundations.
Why this path
Probability is the math course most students complete and least understand. Blitzstein cracks it open by teaching intuition first — the "story" behind every distribution and theorem — which most lecturers consider beneath them. The textbook gives you the reps; Tsitsiklis is the safety net. Skipping the problem sets here is fatal: probability rewards practice more than almost any other math, and lecture watching alone produces fluent-sounding people who cannot solve a basic conditioning problem.