Probability
How to measure uncertainty: from coins and dice to Bayes' theorem and the bell curve.
Measuring uncertainty
Probability as a number between 0 and 1, and the two ways of reading it: long-run frequency and degree of belief.
Outcomes and events
Sample spaces, events, equally likely outcomes, and the counting that turns them into probabilities.
Conditional probability
How learning one fact changes the probability of another: dependence, independence, and the multiplication rule.
Bayes' theorem
The rule for updating a belief with evidence, and why a positive test for a rare disease is often a false alarm.
Random variables and expectation
Attaching numbers to random outcomes, and summarising them with expected value and variance.
Distributions
The shapes chance takes: the uniform, the binomial, and the normal bell curve that appears almost everywhere.