What does the introduction cover?

The intuitive meaning of probability, counting techniques (permutations, combinations, multisets), the classical definition of probability and the addition rule, typical probability problems, conditional probability and independence, and common pitfalls (gambler's fallacy, the Monty Hall problem, the birthday paradox), all at the high school mathematics level.

What background is required?

Basic middle school arithmetic (fractions, simple algebra) and basic set theory (unions, intersections, complements). No calculus is used, so the material is accessible to first-year high school students and to self-learners.

Why are permutations and combinations important for the introduction?

Under the assumption of equally likely outcomes, probability is computed as 'favourable outcomes / total outcomes,' and counting both correctly requires permutations nPr and combinations nCr. Miscounting either makes every probability wrong, so we cover counting before probability proper.

Is Bayes' theorem covered in the introduction?

Bayes' theorem proper is treated at the basics level. The introduction covers the definition of conditional probability P(A|B) and the multiplication rule, then the basics level extends these naturally into Bayes' theorem with axiomatic foundations.

Introduction to Probability

High school level probability

Overview

This introduction covers the probability material taught in high school. We start from the naive question "what is probability?" and build up step by step to counting, the basic laws of probability, and conditional probability.

Learning goals

Build intuition for what probability means.
Count outcomes using permutations and combinations.
Apply the addition and multiplication rules of probability.
Understand conditional probability.
Avoid common pitfalls and misconceptions about probability.

Chapter 1 What Is Probability?
The intuitive meaning of probability, relative frequency, basic properties
Chapter 2 Counting
Permutations $_nP_r$, combinations $_nC_r$, multisets, repeated arrangements
Chapter 3 Definition of Probability
The classical definition, axioms of probability, the addition rule
Chapter 4 Basic Problems
Lotteries, dice, cards — canonical problem patterns
Chapter 5 Conditional Probability
Definition of $P(A|B)$, the multiplication rule, independence
Chapter 6 Common Pitfalls
Gambler's fallacy, the Monty Hall problem, the birthday paradox

Prerequisites

Basic middle school arithmetic (fractions, simple algebra)
Basic set theory (unions, intersections, complements)

Overview

Learning goals

Table of Contents

Prerequisites