A Gentle Introduction to Probability

Massive Open Online Course
  • Overview
  • Course Content
  • Requirements & Materials

A Gentle Introduction to Probability

Course Description

This course provides an introduction to basic probability concepts. Our emphasis is on applications in science and engineering, with the goal of enhancing modeling and analysis skills for a variety of real-world problems.

In order to make the course completely self-contained (and to bring back long-lost memories), we’ll start off with bootcamp lessons to review concepts from set theory and calculus. We’ll then discuss the probability axioms that serve as the basis for all of our subsequent work – what makes probability tick? That discussion will give us the tools to study elementary probability counting rules, including permutations and combinations. We’ll use these rules to work on various cool applications, including poker probability calculations and baseball line-ups!

The next venues on our tour are the concepts of independence and conditional probability, which allow us to see how the probabilities of different events are related to each other, and how new information can be used to update probabilities. The course culminates in a discussion of Bayes Rule and its various interesting consequences related to probability updates.

Course Content



Requirements & Materials



  • Introductory knowledge of set theory and basic calculus
  • Experience in Excel or similar application



  • Internet connection (DSL, LAN, or cable connection desirable)
  • Adobe Acrobat PDF reader (to download for free, visit get.adobe.com/reader/)
  • R statistical software (to download for free, visit cran.r-project.org) (or similar statistics packages such as Minitab, JMP, SAS, etc.)
  • Excel (or equivalent)
  • Bonus software:  Any “real,” high-level language such as MATLAB, Python, etc.


  • All content and course materials available online

Who Should Attend

This course is designed for anyone who needs the tools to understand data, science, philosophy, engineering, economics, and finance.

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What You Will Learn

  • Bootcamp lessons based on set theory and calculus
  • How to identify underlying probability axioms
  • Elementary probability counting rules, including permutations and combinations
  • The concepts of independence and conditional probability
  • How to update probabilities via Bayes Rule
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How You Will Benefit

  • Understand underlying probability axioms.
  • Become familiar with the concepts of independence and conditional probability.
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The course schedule was well-structured with a mix of lectures, class discussions, and hands-on exercises led by knowledgeable and engaging instructors.

- Abe Kani


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