Statistics Foundation · Lesson 3.2
Events, sample spaces and probability rules.
This lesson develops the formal language of probability. Students learn how outcomes form sample spaces, how events work as sets, and how complements, unions, intersections and probability rules allow us to reason carefully about chance.
Lesson route
Move from possible outcomes to formal probability rules.
This lesson is a bridge between intuitive probability and conditional reasoning. Before students can understand conditional probability, they must understand events, overlap, non-overlap, complements and unions.
0–10 min
Outcomes and sample spaces
Define the possible results of a random situation and organise them into a complete sample space.
10–25 min
Events as sets
Understand events as subsets of the sample space and connect probability to set language.
25–45 min
Complements
Study what it means for an event not to happen and derive the complement rule.
45–65 min
Unions and intersections
Use A ∪ B and A ∩ B to describe 'A or B' and 'A and B' carefully.
65–85 min
Addition rule
Derive why P(A ∪ B) = P(A) + P(B) − P(A ∩ B).
85–110 min
Disjoint and overlapping events
Separate mutually exclusive events from overlapping events and avoid double counting.
Mastery checklist
Students should be able to reason with events as mathematical objects.
Define outcome, sample space and event.
Represent events using set notation.
Explain why P(S) = 1 and P(∅) = 0.
Use complements to calculate missing probabilities.
Distinguish union from intersection.
Use the general addition rule correctly.
Identify disjoint events.
Avoid double counting overlapping events.