A Narrative Introduction to Probability

Welcome!

This tutorial teaches probability theory through the story of Chibany (pictured below) who loves tonkatsu and wants to understand how likely they will get it in his daily meals. They hang out at the University cafeteria. Students offer him meals in bento boxes in the hopes that it will help them on their upcoming tests.

Along the way, you’ll learn to think about probability using sets: a perspective that makes complex concepts intuitive and prepares you for probabilistic programming and advanced applications.

Chibany laying down Chibany laying down

Who is this for?

This tutorial was created with designers and social scientists in mind. But it is for anyone wanting to learn about probability, machine learning, and Bayesian thinking in an approachable manner.

No prior math background required: just curiosity and willingness to think carefully!

What you’ll learn

By following Chibany’s journey, you’ll discover:

  • How to think about probability as “counting possibilities”: making abstract concepts concrete
  • The connection between sets and probabilities: a foundation that generalizes to probabilistic programming
  • Conditional probability, independence, and Bayes’ rule: the core tools of probabilistic reasoning
  • How to avoid common misconceptions: through classic puzzles that trip up even experts
  • The foundation for probabilistic computing: the mental models that make code-based approaches make sense

Learning Path

Here’s your journey through probability fundamentals:

graph LR
    A[1. Goals] --> B[2. Chibany's Hungry]
    B --> C[3. Probability & Counting]
    C --> D[4. Conditional Probability]
    D --> E[5. Bayes' Theorem]
    E --> F[6. Glossary]

    style C fill:#4a9eff
    style D fill:#4a9eff
    style E fill:#4a9eff

    classDef foundation fill:#4a9eff,stroke:#333,stroke-width:2px,color:#fff

Core Concepts (blue): The three foundational chapters that build your probability intuition.

Why the set-based perspective?

Most probability courses jump straight into formulas and rules. This tutorial takes a different approach: probability is fancy counting.

When Chibany asks “What’s the probability of getting tonkatsu?”, he’s really asking:

  1. What are all the possibilities? (the outcome space)
  2. Which possibilities include tonkatsu? (the event)
  3. What’s the ratio? (count them!)

This perspective makes conditional probability, Bayes’ rule, and even complex models feel natural instead of mysterious.

A Note on Progress

This tutorial is currently in draft form as part of a planned series. Your feedback is welcome and appreciated! If you find concepts unclear or have suggestions for improvement, please reach out.

Ready to begin?

Let’s meet Chibany and start thinking about probability!

Special thanks to JPPCA for their generous support of this tutorial.

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