Uncertainty
Students learn probability as the formal language used to describe chance, uncertainty and long-run behaviour.
Module 3
Probability Foundations
This module introduces probability as the mathematical language of uncertainty. Students learn sample spaces, events, probability rules, conditional probability, independence, dependence, Bayes’ theorem, expectation and core distribution ideas needed for inference.
Module aim
Build the probability language needed for inference.
Probability is the bridge between descriptive statistics and statistical inference. It helps students understand uncertainty, conditional information, independence and probability-based reasoning before confidence intervals and hypothesis testing.
5
Lessons
Zero
Coding
Foundation
Level
Probability
Focus
Rules
The module builds core probability rules using outcomes, events, complements, unions, intersections and conditions.
Reasoning
Students connect probability to conditional thinking, independence, dependence, Bayes’ theorem and diagnostic interpretation.
Module lessons
Study probability step by step.
Each lesson builds a different part of probabilistic thinking: chance, events, probability rules, conditional information, independence, dependence and updating beliefs using Bayes’ theorem.
3.1
Lesson 3.1
What is probability?
Understand probability as a mathematical language for uncertainty, chance, events and long-run behaviour.
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3.2
Lesson 3.2
Events, sample spaces and probability rules
Learn how outcomes, events, complements, unions, intersections and probability rules are used to reason about chance.
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3.3
Lesson 3.3
Conditional probability
Study how probabilities change when information is known, and why conditional thinking is central to statistics.
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3.4
Lesson 3.4
Independence and dependence
Understand when events are independent, when they are dependent and why this distinction matters in statistical reasoning.
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3.5
Lesson 3.5
Bayes’ theorem and diagnostic reasoning
Learn how Bayes’ theorem connects prior probability, evidence and updated probability using diagnostic-style examples.
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Learning route
Complete probability before studying statistical inference.
Module 4 assumes that students understand events, probability rules, conditional probability, independence, dependence and Bayes’ theorem before moving into sampling distributions, confidence intervals and hypothesis testing.
Continue to Module 4 →Course pathway
Return to the full Statistics Foundation course.
Use the course homepage to move between all five modules, review the full structure and continue through the 26-lesson foundation pathway.
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