Probability

Probability covers the probability scale, theoretical and experimental probability, sample space diagrams, expected frequency, mutually exclusive and independent events, the addition and multiplication rules, tree and Venn diagrams, conditional probability, risk, and the binomial and normal distributions at Higher tier.

The unit rewards drawing. Sample space diagrams and tree diagrams turn awkward problems into counting exercises and make dependent events manageable by forcing each adjusted probability onto the page. Conditional probability is the topic students find hardest, and the key insight is that knowing an event has happened restricts the possibilities to that event, which becomes the new denominator. Common errors include adding probabilities of events that can overlap, treating without-replacement problems as independent, and dividing by the grand total in a conditional question.