The basic topics in this chapter are fundamental to probability theory, and should be accessible to new students of probability. We start with the paradigm of the random experiment and its mathematical model, the probability space. The main objects in this model are sample spaces, events, random variables, and probability measures. We also study several concepts of fundamental importance: conditional probability and independence.

The advanced topics can be skipped if you are a new student of probability, or can be studied later, as the need arises. These topics include the convergence of random variables, the measure-theoretic foundations of probability theory, and the existence and construction of probability measures and random processes.

- Random Experiments
- Events and Random Variables
- Probability Measures
- Conditional Probability
- Independence

- Convergence
- Measure Spaces
- Existence and Uniqueness
- Stochastic Processes
- Filtrations and Stopping Times

- Coin Sample Experiment
- Buffon's Coin Experiment
- Dice Sample Experiment
- Dice Experiment
- Card Sample Experiment
- Die-Coin Experiment
- Coin-Die Experiment
- Venn Diagram App
- Probability Experiment
- Conditional Probability Experiment

- An Introduction to Probability Theory and Its Applications. William Feller
- A First Course in Probability. Sheldon Ross
- The Essentials of Probability. Richard Durrett
- Probability and Measure. Patrick Billingsley
- Probability: Theory and Examples. Richard Durrett
- Games, Gods, and Gambling. Florence David
- History of Mathematics

The most important questions of life are, for the most part, really only problems of probability.

—Pierre Simon Laplace