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Topic 5: Probability

Language of events and sets

4 hours

• Use the concepts and language of outcomes, sample spaces and events as sets of outcomes.
• Use set language and notation for events, including 𝐴 or 𝐴′ for the complement of an event 𝐴, 𝐴 ∩ 𝐵 for the intersection of event 𝐴 and event 𝐵, and 𝐴 ∪ 𝐵 for the union of event 𝐴 and event 𝐵, and recognise mutually exclusive events.
• Use everyday occurrences to illustrate set descriptions and representations of events, and set operations, including the use of Venn diagrams.

Conditional probability and independence

7 hours

• Use the rules 𝑃(𝐴) = 1 − 𝑃(𝐴) and 𝑃(𝐴 ∪ 𝐵) = 𝑃(𝐴)+ 𝑃(𝐵) − 𝑃(𝐴 ∩ 𝐵).
• Understand the notion of a conditional probability and recognise and use language that indicates conditionality.
• Use the notation 𝑃(𝐴|𝐵) and the formula 𝑃(𝐴 ∩ 𝐵) = 𝑃(𝐴|𝐵)𝑃(𝐵) to solve problems.
• Understand and use the notion of independence of an event 𝐴 from an event 𝐵, as defined by 𝑃(𝐴|𝐵) = 𝑃(𝐴). 1 interactive
• Use the formula 𝑃(𝐴 ∩ 𝐵) = 𝑃(𝐴)𝑃(𝐵) for independent events 𝐴 and 𝐵.
• Use relative frequencies obtained from data as point estimates of conditional probabilities and as indications of possible independence of events.
• Model and solve problems that involve probability, with and without technology.