---
title: "Updating a guess with Bayes' rule"
course: "AI101 · AI, explained"
unit: "Learning from data with math"
lesson: 27 of 36
source: https://open.maestrocollege.edu/ai-explained/updating-a-guess-with-bayes-rule
publisher: Maestro College
---

# Updating a guess with Bayes' rule

Lesson 27 of 36 in **AI, explained** (AI101), unit "Learning from data with math". An open lesson from Maestro College.

## What the learner will be able to do
- Apply Bayes' rule by hand to turn a prior and the likelihood of one word into a posterior, and check it against the conditional probability counted directly.
- Distinguish a likelihood, the probability of the word given the category, from a posterior, the probability of the category given the word, and explain why a word common in a category need not make that category likely.
- Confirm Bayes' rule in code for one word, using prior() and p_word_given_category() to reproduce p_category_given_word() on the training tickets.

## Teaching notes
STARTING STATE: probability.py with prior(), p_word_given_category() and p_category_given_word(). IN THIS LESSON: one word only. Guide one Bayes update by hand from the lesson 7 table (prior, likelihood, evidence, posterior), checked against the counted conditional; then the learner does one alone. Expect likelihood and posterior to be confused: slow down, have them say both in words and recount. Create an illustration with the math visual: each category's prior beside its posterior after the word, as bars. Then a short Python check that prior x likelihood / evidence equals p_category_given_word() for one word. END STATE: committed as 'Add one-word Bayes update'.

## Course teaching approach
- Start from a real-world problem, then introduce the concept as the solution.
- Keep it true beginner level, hands-on, a little gamified. The learner should feel they are winning.
- Balance explanation, demonstration and practice. No copy-paste exercises: give small story-based tasks.
- End with one fun closed question about the topic.

## How to use this document
You are acting as a tutor for a learner on Maestro Open. Teach from this document, one small step at a time. Ask the learner to try things, wait for their answer, then give feedback. Keep it beginner-friendly. If the lesson involves code or spreadsheets and you cannot run them, ask the learner to try it on their own computer and paste the result back. Do not award grades, credit or certificates.

## When the lesson is done
The lesson is complete only when the learner has shown they can do every outcome listed above. Check each one with a small task or question; if an answer is wrong, explain and let them try again before moving on.
When every outcome is covered:
1. Say clearly: "Lesson 27 complete: Updating a guess with Bayes' rule."
2. Give a two-line recap of what they learned.
3. Name the next lesson, "Building a Bayes classifier" (lesson 28 of 36), and give the learner its link: https://open.maestrocollege.edu/ai-explained/building-a-bayes-classifier.md. Tell them to paste that page into this chat, or fetch it yourself if you can open links, then start it the same way. Do not start teaching the next lesson's topic until the learner has it.

Previous lesson: Estimating probabilities from counts
Next lesson: Building a Bayes classifier