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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

25

Concepts and
exercises

140+
  1. 1

    Introduction

    Start by understanding and strengthening your existing probabilistic intuition!

    1. Uniform Probabilities

      A tour of the principles of probability and their unusual implications in the world around you.

    2. Counting Cases

      What does it mean for a test to be 90% accurate?

    3. Intro to Simulation

      Simulation can solve problems that would otherwise be out of reach.

  2. 2

    Starting with Probability

    Acquire a few tools to aid you on your probability adventure.

    1. Included with
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      Probabilistic Strategy

      Discover a basic rule of probability and use it to unravel a troubled marketing strategy.

    2. Included with
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      Waiting Time

      Probability can predict more than just how likely an event is.

    3. Included with
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      Common Paradoxes

      A basic rule of probability can help you unravel a surprising paradox.

  3. 3

    Principles of 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
      Brilliant Premium

      Outcome Distributions

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

    3. Included with
      Brilliant Premium

      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.

  4. 4

    Roll the Dice

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

    1. Included with
      Brilliant Premium

      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 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.

  5. 5

    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
      Brilliant Premium

      Barbotte

      Test your knowledge of fairness with a real dice game.

    3. Included with
      Brilliant Premium

      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.