Course: Introduction to Statistics (MATH 11) · Silver Oak University (fictional sample) · Prof. Rivera
Module: Week 5 of 16 · Fall 2026 · in-person, two 75-minute sessions
Objective covered: Objective 4 — Apply basic probability rules, including conditional probability.

This file holds two pieces: (A) the Module 5 Overview page ("Start Here") and (B) the Welcome Announcement that drips out when the module opens. Dates below assume a Tuesday/Thursday session pattern with Week 5 meeting Tue Sep 29 and Thu Oct 1, and end-of-week work due Sunday Oct 4, 11:59 p.m. Adjust the day-of-week and times to match your section.

(A) Module 5 Overview — Start Here

Welcome to Week 5: Probability Foundations

This is your home base for the week. Read it first, then work the checklist below from top to bottom. Everything you need is linked inside the module.

For four weeks we described data we already had — its type, its shape, its center, and how two variables relate. This week the ground shifts: the outcome isn't known yet. A card hasn't been drawn, a test hasn't come back, a game hasn't been played — and our job is to put an honest number on what's likely. A roulette wheel just landed on red eight times in a row; is black now "due"? (No — and by Friday you'll be able to say exactly why.) Probability is the bridge between describing the past and, soon, inferring about the future.

The week's big question

"When the outcome isn't settled yet, how do we put an honest number on what's likely — and how does new information change that number?"

By Friday you'll be able to take any uncertain situation — a card draw, a campus survey, a medical-test result — and compute an honest probability, combine probabilities with the right rule, and update a probability the moment new information arrives.

By the end of this week, you can…

Use this as a checklist. If you can do all four out loud, you're ready for the week's graded work.

• [ ] Write a sample space, name an event, and compute a basic probability as favorable ÷ total — and remember every probability lives between 0 and 1.
• [ ] Apply the complement rule (P(not A) = 1 − P(A)) and the addition rule — knowing when to subtract the overlap and when two events are mutually exclusive so you just add.
• [ ] Apply the multiplication rule for independent events (multiply) — and tell independent from dependent (does one outcome change the other's odds?).
• [ ] Compute a conditional probability P(A | B) from a two-way table or a story, explain what "given" changes, and remember P(A | B) is not P(B | A).

What's due this week, and when

Work these in order — each one gets you ready for the next.

This week's graded set is Quiz 5, Discussion 5, and Assignment 5, plus the weekly Lecture Tutorial.

Heads-up on the AI tutorial and discussion: you'll use a chatbot to draft, and then you judge its work against what we cover in class. Chatbots routinely miss these — they'll forget to subtract the overlap on "King or Heart" (giving 17/52 instead of 16/52), and many fall for the base-rate trap, telling you a positive on a "99%-accurate" test means you're 99% likely to be sick (it's closer to ~17% for a rare disease). Catching the model is the point.

Late policy reminder: 10% off per day late. If life happens, reach out before the deadline — I'd much rather hear from you early.

How to succeed this week

• List the sample space first. The hardest part of any probability problem is writing out everything that could happen. Once the list is right, the answer is just favorable ÷ total. Slow down on the list; the arithmetic is the easy part.
• Memorize three tiny hooks. "'At least one' = 1 minus 'none.'" "OR means add — subtract the overlap unless the events can't coexist." And "AND means multiply — but only when the events are independent."
• Watch the over-1 alarm. A probability can never exceed 1 (or drop below 0). If you compute 1.3, you didn't hit a hard problem — you forgot to subtract an overlap. Re-check.
• "Given" shrinks the world. For a conditional probability, cover up the rest of the two-way table and work inside one row (or one column) — the denominator becomes that subgroup's total, not the grand total. And remember P(A | B) is not P(B | A).
• Treat the chatbot as a smart intern, not an oracle. It'll set up a probability correctly and still double-count an overlap or fall for the base-rate trap. It drafts; you check.

You don't need anything beyond Week 4 for this — just last week's idea of a two-way table, which comes roaring back as the home of conditional probability. Come to class ready to argue about whether anyone is ever really "due" for a win. See you Tuesday.

(B) Welcome Announcement — Module 5

Release setting: post on the module's start day (offset = 0 days), i.e., Tue Sep 29, 2026 — not before. If your platform won't preserve the scheduled date on import, post this as a draft labeled "Release: Tue Sep 29."

Subject: Week 5 — are you ever really "due" for a win? 🎲

Hi everyone,

Quick scene to start: a roulette wheel lands on red eight times in a row. Someone bets big on black — "it has to come now." How much did black's chance actually change? (Answer: not even a little. The wheel has no memory.) That gap — between what feels likely and what is likely — is the whole reason this week exists.

This week — Probability Foundations — we tackle the big question: When the outcome isn't settled yet, how do we put an honest number on what's likely, and how does new information change that number? You'll learn to write a sample space and compute favorable ÷ total, combine chances with the OR rule (add, minus the overlap) and the AND rule (multiply, if the events are independent), and — the big one — compute a conditional probability, the chance of something given that you now know something else.

Two things not to miss:
1. Lecture Tutorial 5 — work through sample spaces, the complement/addition and multiplication rules, and conditional probability with one approved chatbot (Gemini, Claude, or ChatGPT), then submit the share link. You'll catch the model double-counting an overlap or falling for a "99%-accurate test" trap. Due Sun Oct 4.
2. Quiz 5, Discussion 5, and Assignment 5 also close Sun Oct 4 — the discussion is a quick AI dialogue about a real probability misconception ("Due for a win?"), which you summarize and post; start early and leave time to reply to classmates (initial post Fri Oct 2).

A callback to last week: those two-way tables we used for relationships between variables? They're back — this week they become the natural home for conditional probability. The table didn't change; our question got sharper.

Open the Start Here / Module Overview page first — it lays out everything in order with due dates. Bring your curiosity (and an opinion on whether a slot machine is ever really "due" to pay out) to class on Tuesday.

See you soon,
Prof. Rivera