Interactive Course

Applied Probability

A framework for understanding the world around us, from sports to science.

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Overview

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

Interactive quizzes

23

Concepts and exercises

215+

Course map

Prerequisites and Next Steps

  1. 1

    Intro to Probability

    Think probabilistically and explore the wide-reaching applications of probability.

    1. Thinking Probabilistically

      Use probability to avoid logical fallacies and quantify rare events.

      1
    2. Using Outcomes

      Calculate probabilities as fractions of the total count of possible outcomes.

      2
    3. Applications

      Explore applications of probability drawn from physics, meteorology, and tennis!

      3
  2. 2

    Probability Rules

    Get the basics down.

    1. Rule of Sum and Rule of Product

      When do you add probabilities and when do you multiply them?

      4
    2. Inclusion-Exclusion

      Use Venn diagrams to make deductions about probabilities.

      5
    3. The Rule of Complement

      Learn to simplify problems by shifting your perspective to consider the probability an event does NOT happen.

      6
    4. Problem Solving

      Put your probability knowledge to the test solving some real-world problems!

      7
    5. Managing Expectations

      Make choices by comparing the costs and benefits to find the best and worst possible outcomes.

      8
  3. 3

    Conditional Probability

    Update your assumptions with the information around you.

    1. Defining Conditional Probability

      Explore the mathematics that governs the probabilities of dependent events.

      9
    2. Applying Conditional Probability

      Practice calcuating conditional probabilities.

      10
    3. Bayes' Theorem

      How is the probability of A given B related to the probability of B given A?

      11
    4. Misconceptions

      Explore problems where misconceptions commonly arise, including the Monty Hall problem.

      12
    5. Casework

      To understand a complex scenario, systematically split up the big problem into small cases.

      13
    6. Conditional Expectations

      Analyze games that have multiple stages of events and rewards.

      14
  4. 4

    Probability Applications

    Sports, economics, science, and more.

    1. The Tennis Problem

      How is a player's probability of winning a point related to the probability they win the whole game?

      15
    2. Probability in Science

      Apply probability to solve problems in genealogy, cancer research, biology, and physics.

      16
    3. Probability in Economics

      Use probability and expected value to forecast financial futures.

      17
    4. Probability in Quality Control

      Extend what you know about probability to the understand the work potential of assembly lines.

      18
  5. 5

    Advanced Techniques

    Push the frontiers of your knowledge with these probabilistic techniques.

    1. Geometric Probability

      Use geometric reasoning to understand probability distributions of games with infinitely many outcomes.

      19
    2. Bijections

      Discover the surprising power of counting the same thing in two different ways!

      20
    3. Recursion

      Harness the power of knowing a general pattern that relates the early and late values in a sequence.

      21
    4. Markov Chains

      Learn what Markov chains are and use them to model the weather.

      22
    5. Generating Functions

      Explore a clever way to use polynomials to efficiently calculate probabilities.

      23