Key Idea: Probability quantifies how likely an event is, on a scale from 0 (impossible) to 1 (certain). Topic 4.5 builds the core rules: addition rule for combined events, the product rule for independent events, and conditional probability for events that depend on each other. These rules underpin everything in Topics 4.6, 4.8, and 4.9.
✅ Core probability rules
Example: P(A) = 0.4, P(B) = 0.3, P(A∩B) = 0.12 P(A∪B) = 0.4 + 0.3 − 0.12 = 0.58 Are A and B independent? Check: P(A)×P(B) = 0.4×0.3 = 0.12 = P(A∩B). Yes, independent. P(A|B) = P(A∩B)/P(B) = 0.12/0.3 = 0.4 (= P(A), confirming independence) Tree diagram: A bag has 3 red, 2 blue balls. Draw without replacement. P(both red) = (3/5) × (2/4) = 6/20 = 3/10
Use tree diagrams for sequential events (drawing one then another). Multiply along branches (AND) and add across outcomes (OR). When drawing without replacement: the denominator for the second draw decreases by 1, and the available items change depending on the first draw.
Paper 1: Show the formula before substituting. Writing 'P(A∪B) = P(A) + P(B) − P(A∩B)' then substituting earns a method mark separately from the answer. Paper 2: For multi-stage problems, draw a tree diagram even if it takes time — it organises the calculation and prevents combining the wrong branches.