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LearnAQA8300First teaching 2015Papers 1–3 · Foundation tierProbability

Papers 1–3 · Module

Probability

4 subtopics≈ 120 min in total

Start the module: Single events and relative frequency Open graphing calculator

Single events and relative frequency
When outcomes are equally likely, probability $=\dfrac{\text{favourable outcomes}}{\text{total outcomes}}$ . The probabilities of all outcomes add to $1$ , so $P(\text{not }A)=1-P(A)$ . When you can't count outcomes, estimate the probability from experiments: relative frequency.
≈ 25 min
Combined events and tree diagrams
For two independent events, multiply ("and"). For mutually exclusive outcomes, add ("or"). A tree diagram organises both: multiply along each route, then add the routes you want. For "at least one", use $1-P(\text{none})$ .
≈ 35 min
Without replacement and Venn diagrams
When an item is not put back, the second pick has one fewer item, and possibly one fewer of the colour you took. A Venn diagram sorts a group into "only $A$ ", "both", "only $B$ " and "neither": fill in the overlap first.
≈ 30 min
Sets and Venn diagrams
A set is a collection of things, called elements. Venn diagrams draw sets as overlapping circles inside a rectangle (the universal set). Learn the symbols, fill diagrams from the middle outwards, and counting questions become simple bookkeeping.
≈ 30 min