The Bernoulli trials process is one of the simplest, yet most important, of all random processes. It is an essential topic in any course in probability or mathematical statistics. The process consists of independent trials with two outcomes and with constant probabilities from trial to trial. Thus it is the mathematical abstraction of coin tossing. The process leads to several important probability distributions: the binomial, geometric, and negative binomial.

- Introduction
- The Binomial Distribution
- The Geometric Distribution
- The Negative Binomial Distribution
- The Multinomial Distribution
- The Simple Random Walk
- The Beta-Bernoulli Process

- Basic Coin Experiment
- Binomial Coin Experiment
- Binomial Timeline Experiment
- Galton Board Experiment
- Negative Binomial Experiment
- Problem of Points Experiment
- Random Walk Experiment
- Ballot Experiment
- Beta-Binomial Experiment
- Beta-Negative Binomial Experiment

Bernoulli trials appear in many chapters in this project, further evidence of the importance of the model.

- The chapter on Finite Sampling Models includes a number of topics based on a sampling with replacement from a dichotomous population. This type of sampling produces Bernoulli trials.
- The chapter on Games of Chance discusses several games based on Bernoulli trials.
- Estimation of the success parameter is discussed in the chapters on Point Estimation and Set Estimation.
- Hypothesis tests of the success parameter are discussed in the chapter on Hypothesis Testing.

- 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
- A First Course in Probability. Sheldon Ross
- Principles of Random Walk. Frank Spitzer

I didn't major in math; I majored in miracles.

—Mike Huckabee, Republican candidate for President of the US, 2008.