Course: Introduction to Statistics (18-week generic edition)
Module: Week 5 of 18 · planned around two ~75-minute sessions
Objective covered: Objective 4 — Apply probability rules, conditional probability, and random variables to quantify chance (this week: the probability-rules and conditional-probability portion).

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. All timing is relative — "start of Week 5," "end of Week 5" — and maps onto real dates when the adopting instructor sets the term calendar.

(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.

This week the course changes direction. For four weeks you've described data you already had — where it came from, its shape, its center and spread, its relationships. Now we learn to compute the chances of things that haven't happened yet. That machinery — five small rules — is what every inference tool in the second half of the course runs on, and it's also what finally settles the oldest argument at any game table: is anything ever "due"?

The week's big question

"What does 'a 1-in-6 chance' actually promise — and what does it never promise?"

By the end of the week you'll compute chance claims instead of feeling them: NOT, OR, AND, GIVEN — plus the one habit that keeps them honest (asking whether independence is actually plausible before you multiply).

By the end of this week, you can…

Use this as a checklist. If you can do all five out loud, you're ready for the quiz.

• [ ] Say what a probability is — a long-run relative frequency ("probability is a long-run promise, not a short-run guarantee") — and explain what the law of large numbers does and doesn't say.
• [ ] List a sample space and compute equally-likely probabilities (favorable ÷ total) — after checking that "equally likely" is earned, not assumed from "there are two outcomes."
• [ ] Use the complement rule — P(not A) = 1 − P(A) — and keep every answer on the 0-to-1 scale.
• [ ] Use both addition rules and the multiplication rule — "OR adds, then subtracts the overlap"; "AND multiplies, when trials don't talk" — and tell disjoint from independent.
• [ ] Read conditional probabilities from a two-way table — shrink your world to the "given," and never swap P(A | B) with P(B | A).

What to do this week, in order

The table below lists the week's items in working order, with what each is worth and when it's due.

Heads-up on the AI work: in this course the chatbot drafts, and you judge. This week that matters double — chatbots sometimes hedge toward the gambler's fallacy ("well, a six is slightly overdue…") and routinely swap P(A | B) with P(B | A). Catching the model is the point, and this week's lab makes you do exactly that with your own 500 rolls.

Late policy reminder: 10% off per day late. If life happens, reach out to your instructor before the deadline — early is always easier.

How to succeed this week

• Lead with the idea, not the notation. Every rule is a plain-English move first: NOT (the leftovers of 1), OR (add, subtract the overlap), AND (multiply, if independent), GIVEN (shrink your world and re-count). The symbols follow.
• Memorize two tiny hooks. "Probability is a long-run promise, not a short-run guarantee" and "the die has no memory." Between them they defuse the week's two famous traps.
• Run the two reflexes on every answer. Is it between 0 and 1? Can you say it out loud as a long-run statement? An answer of 1.2 isn't confidence — it's a double-count.
• Say the "given" world in words before you divide. "Out of Machine B's 80 widgets…" — that one habit makes P(A | B) vs. P(B | A) impossible to swap.
• Treat the chatbot as a smart intern, not an oracle. It drafts; you check. This week it will be tempted to agree that your six is due. It isn't — and catching that is literally graded in the lab.

You don't need to be a "math person" for this week — every computation is a count and a fraction. Come to the first session with an opinion about lucky streaks; you'll leave with a better one.

(B) Welcome Announcement — Module 5

Release setting: drips at the start of Week 5 (offset = 0 days from module start) — not before. If your platform won't preserve the scheduled release on import, post it as a draft labeled "Release: start of Week 5."

Subject: Welcome to Week 5 — is anything ever "due"?

Hi everyone,

Quick story before the week starts. One night in 1913, at a Monte Carlo roulette table, black came up twenty-six times in a row. As the streak grew, bettors piled fortunes on red — it had to be due — and the wheel, which had no memory of any of it, took everything. This week you learn exactly why they lost, and why the same reasoning quietly costs people money, points, and arguments every day.

This week — Probability Foundations — we tackle the big question: What does "a 1-in-6 chance" actually promise — and what does it never promise? Last week you finished the describing-data half of the course with two-way tables and the correlation-isn't-causation warning. Now those same tables become probability machines, and five small rules — NOT, OR, AND, GIVEN, plus the 0-to-1 scale — turn chance from a feeling into a computation.

Three things not to miss:
1. Chapter 5 is your primary reading — start there; every rule arrives with a worked example you'll reuse all week.
2. Data Lab 5 has you roll a virtual die 500 times in your spreadsheet and watch the long run keep its promise live on your screen — then catch your chatbot if it flirts with the "it's due" fallacy. Due at the end of Week 5.
3. Discussion 5 — "The Lucky Streak Problem" — wants the chance belief you actually hold (a lucky ritual, a due number, a hot streak) interrogated with this week's tools. Initial post two days before the week ends, so classmates have time to reply.

Also in the module: Lecture Tutorial 5 (your AI tutor drills all five rules — submit the share link and summary), quick ungraded practice, Quiz 5 (closed to AI), and Assignment 5 — "What Are the Odds?"

One promise: nothing this week needs more math than counting and fractions. The hard part isn't calculation — it's unlearning what your gut insists about streaks. Open the Start Here / Module Overview page first — it lays out everything in order with due points.

See you in the course!