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Probability Fundamentals

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Probability Fundamentals provided by Brilliant is a comprehensive online course, which lasts for 4 hours worth of material. Upon completion of the course, you can receive an e-certificate from Brilliant. The course is taught in Englishand is Paid Course. Visit the course page at Brilliant for detailed price information.

via Brilliant
4 hours worth of material
Self Paced
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.
    Only foundational-level algebra is used in this course and no prior probability background is required!

Syllabus

    • Introduction: Start by understanding and strengthening your existing probabilistic intuition!
      • Uniform Probabilities: A tour of the principles of probability and their unusual implications in the world around you.
      • The Rule of Sum: Discover a basic rule of probability and use it to unravel a troubled marketing strategy.
      • Probable Past & Future: Probability can guide our decisions, whether it’s the future or making sense of the uncertain past.
    • Starting With Probability: What are the odds of getting all these problems right?
      • Using Outcomes: Strengthen your intuition for probabilistic math by thinking systematically about outcomes.
      • Outcome Distributions: Learn how to create and use distribution charts to tackle challenging problems.
      • Complements: Learn how and when to switch perspectives and ask, "When does this event NOT happen?".
      • Expected Value: Practice making smart, strategic decisions, even when the outcomes are uncertain.
      • Games & Gambling: Analyze lotteries, coin flips, and other games of chance to learn how probability can help you avoid costly mistakes.
    • Roll the Dice: Roll the dice! Take a chance! But know what the risk is.
      • The Rules of Sum and Product: Get starting using dice to explore the Rule of Sum and Rule of Product.
      • Common Intuitive Fallacies: Avoid the pitfalls of probability in situations where mistakes are common.
      • Complementary Probabilities: When is it easier to find the probability of something NOT happening?
      • Using Symmetry: When things are balanced, you can use these shortcuts.
      • Endgame Strategy: Approach the real game of Shut the Box and find the best strategies!
    • Fairness and Expected Value: Evaluate games and their fairness.
      • Introduction to Fairness: When do players have an equal chance of winning?
      • Barbotte: Test your knowledge of fairness with a real dice game.
      • Roulette: Calculate some bets on the classic casino game.
      • Piglet: Untangle the strategies behind this progressive dice game.
      • Linearity of Expectation: Sometimes, adding the expected values is all you need to do.
      • Bunco: Use math and decide: should you play this game?
      • Symmetry: Leverage symmetry in creative and surprising ways.
      • Stein's Game: A simple game with cards leads to a tricky probability scenario.
      • Information Asymmetry: Knowing more information can significantly change the probabilities.

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