Title: Week 5 Overview — Start Here
Course: Introduction to Statistics (18-Week Generic Edition)

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.

# | Do this | Type | Due
1 | Read Chapter 5 — the module's primary reading | Chapter (ungraded prep) | Early in the week
2 | Skim the slides (Deck 5) and the Week 5 lecture outline; browse the Readings & Resources links that interest you | Prep (ungraded) | Alongside class
3 | Lecture Tutorial 5 — work the five rules with your chatbot, then submit the share link + Completion Summary | Tutorial · graded (Lecture tutorials, 20% group) | End of Week 5
4 | Practice exercises — quick reps with the AI coach | Practice · ungraded | Before the quiz (recommended)
5 | Data Lab 5 — "The Long Run: 500 Rolls of a Virtual Die" — simulate 500 rolls with =RANDBETWEEN(1,6) and watch the law of large numbers happen on your own screen | Data lab · graded (Data labs, 15% group) | End of Week 5
6 | Quiz 5 — the five rules, disjoint vs. independent, the gambler's fallacy, conditional probability | Quiz · graded (Quizzes, 15% group) · closed to AI | End of Week 5
7 | Discussion 5 — "The Lucky Streak Problem" — interrogate a chance belief you actually hold in a dialogue with your chatbot, post the AI summary + chat link, then reply to two classmates | Discussion · graded (Discussions, 15% group) | Initial post two days before week's end; replies by end of Week 5
8 | Assignment 5 — "What Are the Odds?" — four AI-coached problems; submit the report (score on line 1) + chat link | Assignment · graded (Assignments, 25% group) | End of Week 5

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.