--- title: Discrete Probability description: Discrete probability deals with random variables that have countable outcomes. Learners will understand how to calculate likelihoods, analyze random events, and apply probability distributions to computer science, combinatorics, and game theory. category: mathematics subcategory: discrete-math difficulty: beginner, intermediate, advanced url: /subject/discrete-probability --- # Discrete Probability Discrete probability deals with random variables that have countable outcomes. Learners will understand how to calculate likelihoods, analyze random events, and apply probability distributions to computer science, combinatorics, and game theory. ## Available Resources 1 Books • 4 Courses • 2 Websites ## Websites ### 1. Art of Problem Solving - Probability Art of Problem Solving wiki entry on probability for competition math students: defines outcomes, events, and basic probability rules, then lists introductory, intermediate, and olympiad contest problems linked to worked solutions. Good for practicing discrete probability problem-solving. **Difficulty:** Beginner | **Price:** Free **Link:** https://artofproblemsolving.com/wiki/index.php/Probability **Tags:** probability, discrete-probability, competition-math, counting, problem-solving ### 2. probabilitycourse.com ProbabilityCourse.com is an online learning resource that provides a structured probability course with clear explanations, worked examples, and practice problems covering topics from basics to advanced theory. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://probabilitycourse.com **Tags:** websites, technology-computer-science, data-science--ai ## Courses ### 1. Discrete Probability Learn discrete probability concepts like counting, permutations, and conditional probability. Build your skills with this comprehensive course! **Difficulty:** Beginner | **Price:** Free **Link:** https://www.khanacademy.org/math/statistics-probability/probability-library **Tags:** probability, discrete-probability, combinatorics, conditional-probability ### 2. Probabilistic Systems Analysis and Applied Probability (MIT 6.041SC) **Author:** John Tsitsiklis Modeling and analysis of uncertainty: probability models, discrete and continuous random variables, Bayesian inference, limit theorems and random processes. Designed for independent study, with lecture videos, slides, recitation and tutorial problems, problem sets and exams with solutions, and TA problem-solving videos. **Difficulty:** Intermediate | **Price:** Free **Link:** https://ocw.mit.edu/courses/6-041sc-probabilistic-systems-analysis-and-applied-probability-fall-2013/ **Tags:** probability, random-variables, bayesian-inference, limit-theorems, random-processes, statistical-inference ### 3. Introduction to Probability **Author:** Joe Blitzstein HarvardX's self-paced version of Harvard's Stat 110, taught by Joe Blitzstein. Covers counting and story proofs, conditional probability and Bayes' rule, discrete and continuous random variables, joint distributions, the law of large numbers, the central limit theorem and Markov chains. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://www.edx.org/learn/probability/harvard-university-introduction-to-probability **Tags:** probability, random-variables, bayes-rule, probability-distributions, markov-chains, central-limit-theorem ### 4. Discrete Mathematics **Author:** Dominik Scheder Dominik Scheder's proof-based course on sets, functions and relations, enumerative combinatorics, graph theory, and network flows and matchings, each concept paired with a fully proved non-trivial result. Learners read formal statements and write rigorous proofs of their own. **Difficulty:** Intermediate | **Language:** English | **Duration:** 11 weeks of study, 3-5 hours per week. | **Price:** Free **Link:** https://www.coursera.org/learn/discrete-mathematics **Tags:** discrete-math, combinatorics, graph-theory, network-flows, proofs ## Books ### 1. Probability and Random Processes **Author:** Geoffrey Grimmett, David Stirzaker Rigorous textbook on probability and stochastic processes, from discrete and continuous random variables, generating functions, and limit theorems through Markov chains, martingales, stationary processes, and diffusions, with extensive exercises. Builds measure-aware probabilistic reasoning for graduate study or quantitative research. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0198572220?tag=edmonddante07-20 **Tags:** books, mathematics-statistics, discrete-math --- *This content is part of Dantes.io - Your Treasure Map to Knowledge* *Curated by humans at Dantes.io. Personal study use welcome; republishing this curation requires permission (team@dantes.io).* View this page online: https://dantes.io/subject/discrete-probability