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What you will learn in Probability
1. Randomness, Chance and Relative Frequency
What probability promises — that relative frequency settles — and the two things it never promises.
2. Sample Spaces and Events
Every outcome laid out, an event as a subset, and a probability read off as a cell count.
3. Classical Probability by Counting
Favourable over total, when every outcome is equally likely — and the counting comes from module 10.
4. The Addition Rule and Complements
One rule for 'or', with the overlap subtracted — and the complement as the shortcut it usually is.
5. Conditional Probability
Conditioning is restriction: cross out what did not happen and count what remains.
6. Multiplication Rule and Independence
Independence is tested, not assumed. And mutually exclusive is its opposite, not its cousin.
7. Tree Diagrams and Two-Way Tables
Multiply along the branches, add across the paths — and watch replacement change everything.
8. Bayes' Theorem
A 99%-accurate test for a rare disease, and why a positive result usually means you are fine.
9. Discrete Random Variables
A distribution table, and the check that has to pass before anything can be computed from it.
10. Expectation and Variance
The balance point of a distribution — which need not be a value the variable can take.
11. The Binomial Distribution
Module 10's expansion with probabilities substituted — and the four conditions it needs.
12. The Poisson Distribution (Introduction)
Counting rare events over an interval, and where it comes from as a binomial limit.
13. The Normal Distribution
Area under a curve as probability, computed rather than looked up — and what 68–95–99.7 really is.
14. Simulation and the Law of Large Numbers
What simulation can establish, what it cannot, and the sentence that has to accompany every simulated number.