Applied Probability

Tap into a framework for understanding the world around us, from sports to science.

Thinking Probabilistically

Using Outcomes


Rule of Sum and Rule of Product


The Rule of Complement

Problem Solving

Managing Expectations

Defining Conditional Probability

Applying Conditional Probability

Bayes' Theorem



Conditional Expectations

The Tennis Problem

Probability in Science

Probability in Economics

Probability in Quality Control

Geometric Probability



Markov Chains

Generating Functions

Course description

How can we accurately model the unpredictable world around us? How can we reason precisely about randomness? This course will guide you through the most important and enjoyable ideas in probability to help you cultivate a more quantitative worldview. By the end of this course, you’ll master the fundamentals of probability, and you’ll apply them to a wide array of problems, from games and sports to economics and science.

Topics covered

  • Bayes' Theorem
  • Complementary Probabilities
  • Conditional Probability
  • Economic Applications
  • Expected Value
  • Inclusion-Exclusion
  • Independent Events
  • Markov Chains
  • Probability Misconceptions
  • Recursion
  • Science Applications
  • The Monty Hall Problem

Prerequisites and next steps

You'll need an understanding of basic algebra, including functions. For a lighter introduction to probability, see the Casino Probability course.


  • Introduction to Probability