Mathematics — first biennium · Lesson
With two independent trials it helps to build the sample space. The complement often simplifies 'at least one' events.
Prerequisites: Classical probability and sets
Goal: Build compound sample spaces and use complementary events.
In this lesson: Build compound sample spaces and use complementary events.
New concept: In a multi-stage experiment, each branch of the tree represents a successive choice/outcome. Probabilities along one path are multiplied; probabilities of alternative compatible paths are added.
How to proceed: Write HH, HT, TH, TT before counting. For 'at least one' you can also subtract the case where it never occurs from 1.
You can already assume: Classical probability and sets.
E₁: H · E₂: T
The tree shows the four ordered outcomes of two tosses and makes complement checking immediate.
Completed exercises: 0/5 · Correct on first attempt: 0
Write HH, HT, TH, TT before counting. For 'at least one' you can also subtract the case where it never occurs from 1.
Data / situation: Two tosses of a fair coin: get two heads.
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.