Mathematics — first biennium · Lesson
Events are sets of outcomes. The union contains outcomes belonging to at least one event; the intersection contains common outcomes; the complement contains outcomes outside the event but inside Ω.
Prerequisites: Compound events and set operations
Goal: Use union, intersection and complement to describe events and calculate their probabilities in simple equally likely spaces.
In this lesson: Use union, intersection and complement to describe events and calculate their probabilities in simple equally likely spaces.
New concept: A∪B means ‘A or B’ and includes the intersection; A∩B means ‘A and B together’; the complement Aᶜ contains outcomes where A does not occur. To avoid double-counting the intersection: P(A∪B)=P(A)+P(B)−P(A∩B).
How to proceed: First place outcomes in the four regions: A only, intersection, B only, and outside both. Then count them out of the six equally likely outcomes.
You can already assume: Compound events and set operations.
A: A = even number · B: B = number at least 4
The Venn diagram makes union, intersection and complement relative to Ω visible at the same time.
Completed exercises: 0/5 · Correct on first attempt: 0
First place outcomes in the four regions: A only, intersection, B only, and outside both. Then count them out of the six equally likely outcomes.
Data / situation: A fair die is rolled. A = even number; B = number at least 4.
ConceptStep separates what is required from what is recommended or useful as reinforcement. Only required prerequisites block your progress.
Relationships: solid line = required · dashed line = recommended · dotted line = reinforcement.