01
Sample spaces and the axioms
What is a probability a probability of?
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Statistics 110: Probability ↗Joe Blitzstein, Harvard
Free full course, textbook and problem sets. Exceptional teaching.
Core · Module 07
Probability
Probability is where careful people are wrong most often. Build it axiomatically and the paradoxes stop being paradoxes.
By the end of this module
You can reason correctly about uncertainty — including the cases where everyone's intuition fails.
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02
Conditional probability and Bayes' theorem
How should evidence change what I believe?
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Bayes' rule: guide ↗Arbital
A guided, branching explanation that adapts to what confuses you.
03
Random variables and distributions
Why do so few distributions describe so much?
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Seeing Theory ↗Brown University
Every concept as a manipulable animation. Beautiful and genuinely useful.
04
Law of large numbers and the central limit theorem
Why is the bell curve everywhere?
Check yourself
End-of-module quiz
Every answer comes with the reasoning, not just a verdict. Getting one wrong and reading why is the point.
01A disease affects 1 in 1000. A test is 99% accurate both ways. You test positive. Roughly what is the chance you have it?
02The central limit theorem requires that the underlying distribution be:
03Two events A and B are independent if:
Answer all 3 to finish the module.