Probability

Sections

1. 14A Sets and Venn diagrams Set notation, equal sets, the size of a set, the empty set, union and intersection, subsets, complements, Venn diagrams and the counting rule.
2. 14B Probability and sample spaces Random experiments, equally likely outcomes, the formula P(E) = |E|/|S|, playing cards, impossible and certain events, complements, invalid arguments and relative frequency.
3. 14C Sample space graphs and tree diagrams Listing outcomes of multi-stage experiments with a grid or a tree diagram, and using complements such as "at least one".
4. 14D Venn diagrams and the addition theorem Mutually exclusive events, the addition theorem P(A ∪ B) = P(A) + P(B) − P(A ∩ B), and using Venn diagrams for "or" questions.
5. 14E Multi-stage experiments and the product rule Independent events, the product rule P(A ∩ B) = P(A) × P(B) for multi-stage experiments, and "at least one" problems.
6. 14F Probability tree diagrams Building probability trees with probabilities on the branches, multiplying along paths and adding paths, with and without replacement.
7. 14G Conditional probability Reduced sample spaces, the formula P(A | B) = P(A ∩ B) / P(B), the general product rule, independence, and two-way tables.