Interactive Course

Probability Fundamentals

Begin your study of probability with this course.

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Overview

Life is full of all sorts of risks, chances, and gambles.

With this course, you'll learn to analyze probabilistic scenarios and optimize your chances to win probabilistic games. By the end of this course, you’ll have mastered many foundational topics including fairness, expected value, and using symmetry to simplify probability problems.

Topics covered

  • Complements
  • Expected Value
  • Fairness
  • Linearity of Expectation
  • Probability Misconceptions
  • Roulette Strategy
  • Rule of Sum
  • Rule of Product
  • Shut the Box
  • Symmetry

Interactive quizzes

22

Concepts and exercises

135+

Course map

Prerequisites and Next Steps

  1. 1

    Introduction

    Start by understanding and strengthening your existing probabilistic intuition!

    1. Test Your Probabilistic Intuition

      How closely does your intuition match reality?

      1
    2. Common Fallacies

      Learn to avoid some very common types of mistakes.

      2
    3. Counting and Probability

      There's an essential and fundamental connection between counting problems and probability problems.

      3
  2. 2

    Starting With Probability

    What are the odds of getting all these problems right?

    1. Using Outcomes

      Strengthen your intuition for probabilistic math by thinking systematically about outcomes.

      4
    2. Outcome Distributions

      Learn how to create and use distribution charts to tackle challenging problems.

      5
    3. Complements

      Learn how and when to switch perspectives and ask, "When does this event NOT happen?".

      6
    4. Expected Value

      Practice making smart, strategic decisions, even when the outcomes are uncertain.

      7
    5. Games & Gambling

      Analyze lotteries, coin flips, and other games of chance to learn how probability can help you avoid costly mistakes.

      8
  3. 3

    Roll the Dice

    Roll the dice! Take a chance! But know what the risk is.

    1. The Rules of Sum and Product

      Get starting using dice to explore the Rule of Sum and Rule of Product.

      9
    2. Common Intuitive Fallacies

      Avoid the pitfalls of probability in situations where mistakes are very common.

      10
    3. Complementary Probabilities

      When is it easier to find the probability of something NOT happening?

      11
    4. Using Symmetry

      When things are balanced, you can use these shortcuts.

      12
    5. Endgame Strategy

      Approach the real game of Shut the Box and find the best strategies!

      13
  4. 4

    Fairness and Expected Value

    Evaluate games and their fairness.

    1. Introduction to Fairness

      When do players have an equal chance of winning?

      14
    2. Barbotte

      Test your knowledge of fairness with a real dice game.

      15
    3. Roulette

      Calculate some bets on the classic casino game.

      16
    4. Piglet

      Untangle the strategies behind this progressive dice game.

      17
    5. Linearity of Expectation

      Sometimes, adding the expected values is all you need to do.

      18
    6. Bunco

      Use math and decide: should you play this game?

      19
    7. Symmetry

      Leverage symmetry in creative and surprising ways.

      20
    8. Stein's Game

      A simple game with cards leads to a tricky probability scenario.

      21
    9. Information Asymmetry

      Knowing more information can significantly change the probabilities.

      22