•  Simulation of Discrete Probabilities
•  Discrete Probability Distributions

•  Simulation of Continuous Probabilities
•  Continuous Density Functions

•  Permutations
•  Combinations
•  Card Shuffling

•  Discrete Conditional Probability
•  Continuous Conditional Probability
•  Paradoxes

5. Distributions and Densities

•  Important Distributions
•  Important Densities

•  Expected Value
•  Variance of Discrete Random Variables
•  Continuous Random Variables

•  Sums of Discrete Random Variables
•  Sums of Continuous Random Variables

•  Discrete Random Variables
•  Continuous Random Variables

•  Bernoulli Trials
•  Discrete Independent Trials
•  Continuous Independent Trials

10. Generating Functions

•  Discrete Distributions
•  Branching Processes
•  Continuous Densities

11. Markov Chains

•  Absorbing Markov Chains
•  Ergodic Markov Chains
•  Fundamental Limit Theorem
•  Mean First Passage Time

•  Random Walks in Euclidean Space
•  Gambler's Ruin
•  Arc Sine Laws

Probability theory began in seventeenth century France when the two great French mathematicians, Blaise Pascal and Pierre de Fermat, corresponded over two problems from games of chance. Problems like those Pascal and Fermat solved continued to influence such early researchers as Huygens, Bernoulli, and DeMoivre in establishing a mathematical theory of probability. Today, probability theory is a well established branch of mathematics that nds applications in every area of scholarly activity from music to physics, and in daily experience from weather prediction to predicting the risks of new medical treatments.

Probability is a wonderfully intuitive and applicable field of mathematics. We have tried not to spoil its beauty by presenting too much formal mathematics. Rather, we have tried to develop the key ideas in a somewhat leisurely style, to provide a variety of interesting applications to probability, and to show some of the nonintuitive examples that make probability such a lively subject.

This book is distributed on the Web as part of the Chance Project, which is devoted to providing materials for beginning courses in probability and statistics.  Specifically, it is a version of Grinstead and Snell's Introduction to Probability, 2nd edition, published by the American Mathematical Society, Copyright (C) 2003 Charles M. Grinstead and J. Laurie Snell. This work is freely redistributable under the terms of the GNU Free Documentation License.