Probability Fundamentals

Take a chance and explore the math of unpredictability.

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.

Interactive
quizzes

22

Concepts and
exercises

135+
  1. 1

    Introduction

    Start by understanding and strengthening your existing probabilistic intuition!

    1. Test Your Probabilistic Intuition

      How closely does your intuition match reality?

    2. Common Fallacies

      Learn to avoid some very common types of mistakes.

    3. Counting and Probability

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

  2. 2

    Starting With Probability

    What are the odds of getting all these problems right?

    1. Included with
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      Using Outcomes

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

    2. Included with
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      Outcome Distributions

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

    3. Included with
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      Complements

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

    4. Included with
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      Expected Value

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

  3. 3

    Roll the Dice

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

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      The Rules of Sum and Product

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

    2. Included with
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      Common Intuitive Fallacies

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

    3. Included with
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      Complementary Probabilities

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

    4. Included with
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      Using Symmetry

      When things are balanced, you can use these shortcuts.

  4. 4

    Fairness and Expected Value

    Evaluate games and their fairness.

    1. Included with
      Brilliant Premium

      Introduction to Fairness

      When do players have an equal chance of winning?

    2. Included with
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      Barbotte

      Test your knowledge of fairness with a real dice game.

    3. Included with
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      Roulette

      Calculate some bets on the classic casino game.

    4. Included with
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      Piglet

      Untangle the strategies behind this progressive dice game.