https://josephausterweil.github.io/probintro/foundations/index.htmlWill there be tonkatsu today? It is April, a new school year at Chiba Tech, and the campus mascot Chibany has one consuming question about the two bentos students bring them every day. This Part builds all of probability out of that question — by counting. Sets of possible days, events as subsets, conditioning as crossing out possibilities, and Bayes’ rule as the inevitable arithmetic of updating.Hugoen-usThu, 02 Jul 2026 00:00:00 +0000https://josephausterweil.github.io/probintro/foundations/hungry/index.htmlThu, 02 Jul 2026 00:00:00 +0000https://josephausterweil.github.io/probintro/foundations/hungry/index.htmlChibany wakes up from dreaming of the delicious meals they will get later today. Twice per day, a student brings them a bento box with a meal as an offering to Chibany. One student brings them a bento box in the early afternoon for lunch and a different student brings them a bento box in the evening for dinner. The meal is either a Hamburger or a Tonkatsu (pork cutlet) . To keep track of their meal possibilities, they list out the four possibilities:https://josephausterweil.github.io/probintro/foundations/probability-as-counting/index.htmlThu, 02 Jul 2026 00:00:00 +0000https://josephausterweil.github.io/probintro/foundations/probability-as-counting/index.htmlOne goal of this tutorial is to show you that probability is counting. When every possible outcome is equally likely, the probability of an event $A$ is the fraction of the whole outcome space that lands inside $A$ — the count of outcomes in $A$ divided by the count of all possible outcomes: $$P(A) = \frac{|A|}{|\Omega|},$$where $\Omega$ (Greek capital omega) is the set of all possible outcomes. When outcomes are not equally likely, it is only slightly more complicated: instead of each outcome counting one, each contributes its own weight, and you compare total weights the same way. We come back to the weighted case below.https://josephausterweil.github.io/probintro/foundations/conditional-probability/index.htmlThu, 02 Jul 2026 00:00:00 +0000https://josephausterweil.github.io/probintro/foundations/conditional-probability/index.htmlThe Big Question Have you ever changed your mind about something after learning new information? Of course you have! That’s what conditional probability is all about: how new knowledge changes what we believe is possible. In this chapter, you’ll discover: How learning something restricts the outcome space When events influence each other (dependence) How to calculate probabilities when possibilities have different weights Why your first intuition about conditional probability is often wrong! Ready for some surprising results? Let’s see what Chibany learns about dinner…https://josephausterweil.github.io/probintro/foundations/bayes-rule/index.htmlThu, 02 Jul 2026 00:00:00 +0000https://josephausterweil.github.io/probintro/foundations/bayes-rule/index.htmlThe Most Surprising Result in Probability Prepare to have your intuition completely shattered. 🤯 You’re about to discover why a positive medical test doesn’t mean what you think, why eyewitness testimony is less reliable than you expect, and why one of the most famous problems in probability stumps even experts. In this chapter, you’ll learn: How Bayes’ theorem updates beliefs with evidence Why base rates matter more than accuracy How to avoid the cognitive trap that catches almost everyone Why your first answer to the Taxicab Problem is almost certainly wrong! Fair warning: After this chapter, you’ll question your intuition about probabilities forever. Ready? Let’s meet Chibany on a foggy night…https://josephausterweil.github.io/probintro/foundations/glossary/index.htmlThu, 02 Jul 2026 00:00:00 +0000https://josephausterweil.github.io/probintro/foundations/glossary/index.htmlThis glossary provides definitions for key terms used throughout the tutorial. Click on any term to expand its definition. Core Concepts set set A set is a collection of elements or members. Sets are defined by the elements they do or do not contain. The elements are listed with commas between them and “$\{$” denotes the start of a set and “$\}$” the end of a set. Note that the elements of a set are unique.