--- title: Probability description: Probability is the mathematical study of uncertainty and randomness. Learners will understand random variables, probability distributions, Bayes' theorem, and how to calculate the likelihood of events to inform decision-making and statistical models. category: programming-tech subcategory: data-science difficulty: beginner, intermediate, advanced url: /subject/probability --- # Probability Probability is the mathematical study of uncertainty and randomness. Learners will understand random variables, probability distributions, Bayes' theorem, and how to calculate the likelihood of events to inform decision-making and statistical models. ## Available Resources 2 Videos • 4 Books • 5 Courses • 3 Websites ## Videos ### 1. Bayes Theorem, the geometry of changing beliefs Grant Sanderson builds Bayes' theorem from a diagram of overlapping populations rather than the formula, using the medical-test and Steve-the-librarian examples. Viewers finish able to reason about how evidence should shift a prior probability. **Difficulty:** Beginner | **Price:** Free **Link:** https://www.youtube.com/watch?v=HZGCoVF3YvM **Tags:** bayes-theorem, conditional-probability, visual-intuition, statistics ### 2. Binomial distributions | Probabilities of probabilities, part 1 Animated walkthrough of the binomial distribution, using a product-review example to show how observed successes and failures translate into a probability density over an unknown underlying success rate. Explains where the binomial coefficient comes from. **Difficulty:** Beginner | **Price:** Free **Link:** https://www.youtube.com/watch?v=8idr1WZ1A7Q **Tags:** probability, binomial-distribution, bayesian-inference, visual-math ## Courses ### 1. Information Theory (MIT 6.441) **Author:** Yury Polyanskiy Graduate introduction to the mathematics of information: entropy, lossless compression, binary hypothesis testing, channel coding and lossy compression. Provides 29 lecture note files that together form a textbook-length treatment, plus problem sets. Prepares you to state and prove the core coding theorems. **Difficulty:** Advanced | **Price:** Free **Link:** https://ocw.mit.edu/courses/6-441-information-theory-spring-2016/ **Tags:** information-theory, entropy, data-compression, channel-coding, probability ### 2. Statistics 110: Probability Learn probability fundamentals with Harvard's Statistics 110 course, taught by Joe Blitzstein. Perfect for building a strong statistical foundation! **Difficulty:** Beginner | **Price:** Free **Link:** https://www.youtube.com/playlist?list=PL2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo **Tags:** probability, conditional-probability, random-variables, markov-chains ### 3. 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 ### 4. An Intuitive Introduction to Probability **Author:** Karl Schmedders University of Zurich course taught by Karl Schmedders that builds probability from everyday examples: basic rules, conditional probability, applications, discrete random variables, and the normal distribution. Learners finish able to compute and interpret probabilities in practical decisions. **Difficulty:** Beginner | **Language:** English | **Price:** Free **Link:** https://www.coursera.org/learn/introductiontoprobability **Tags:** probability, conditional-probability, discrete-random-variables, normal-distribution ### 5. 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 ## Books ### 1. Introduction to Probability **Author:** Joseph K. Blitzstein, Jessica Hwang Learn the fundamentals of probability with this introductory book by Blitzstein & Hwang. Perfect for statistics beginners! **Difficulty:** Beginner | **Price:** Paid **Link:** https://www.amazon.com/dp/1466575573?tag=edmonddante07-20 **Tags:** probability, random-variables, probability-distributions, conditional-probability ### 2. Probability **Author:** Geoffrey Grimmett, David Stirzaker Graduate-level treatment of probability theory and stochastic processes, covering measure-theoretic foundations, generating functions, Markov chains, martingales and diffusion. Working the exercises builds the machinery needed for research in stochastic processes and mathematical statistics. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0198531850?tag=edmonddante07-20 **Tags:** books, mathematics-statistics, mathematics ### 3. A First Course in Probability **Author:** Sheldon Ross Standard undergraduate textbook covering combinatorial analysis, conditional probability, discrete and continuous random variables, expectation, and limit theorems. Its large graded problem sets train you to set up and solve probability calculations from scratch. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0130338516?tag=edmonddante07-20 **Tags:** books, technology-computer-science, data-science--ai ### 4. Fifty Challenging Problems **Author:** Frederick Mosteller A compact Dover collection of fifty probability puzzles with full worked solutions, chosen by a Harvard statistician for the techniques they teach. Working them sharpens your ability to model messy word problems as tractable calculations. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0486653552?tag=edmonddante07-20 **Tags:** books, mathematics-statistics, mathematics ## Websites ### 1. 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 ### 2. seeing-theory.brown.edu Seeing Theory is an interactive, browser-based resource from Brown University that uses visual simulations to explain fundamental probability and statistics concepts. It offers interactive demos and explanations on topics like probability, distributions, sampling, the central limit theorem, confidence intervals, hypothesis testing, and Bayesian reasoning. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://seeing-theory.brown.edu **Tags:** websites, technology-computer-science, data-science--ai ### 3. statlect.com Statlect is a free online resource with comprehensive lecture notes on probability and statistics. It covers topics from basic probability, random variables, and distributions to inference, hypothesis testing, and Bayesian methods, featuring formal explanations and worked examples. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://statlect.com **Tags:** websites, technology-computer-science, data-science--ai --- *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/probability