Probability
The rules of chance, conditional probability and Bayes' theorem.
Sample spaces and events, the addition and multiplication rules, conditional probability and independence, probability trees, Bayes' theorem, counting and expected value — with simulations that compare theory with observed frequencies.
Lessons
- 1Sample spaces and eventsDescribe a random experiment by its sample space and events, and compute probabilities by counting equally likely outcomes or from long-run relative frequencies.25 minFree
- 2Probability rulesUse the complement rule and the addition rule correctly, and recognise when events are mutually exclusive.30 minMembers
- 3Conditional probabilityCalculate conditional probabilities from two-way tables and from probabilities, and read the condition the right way round.30 minMembers
- 4IndependenceDecide whether two events are independent, use the product rule only when it applies, and never confuse independent with mutually exclusive.30 minMembers
- 5Multiplication rule and probability treesUse the general multiplication rule and probability trees to find probabilities of sequences of events, and combine branches with the law of total probability.30 minMembers
- 6Bayes' theoremUse Bayes' theorem and natural frequencies to turn P(evidence | hypothesis) into P(hypothesis | evidence), and explain why base rates matter.35 minMembers
- 7Counting: permutations and combinationsCount outcomes with the multiplication principle, permutations and combinations, and use the counts to find probabilities.30 minMembers
- 8Expected value and variance of a random payoffCompute the expected value, variance and standard deviation of a random payoff, and judge when expected value is — and is not — a good basis for a decision.30 minMembers
- 9Theory versus simulationEstimate probabilities by simulation, explain the law of large numbers, and judge how far an observed frequency can reasonably be from the true probability.30 minMembers