Week 5 — Readings & Resources · Probability Foundations

Course: Introduction to Statistics (MATH 11) · Silver Oak University (fictional sample) · Prof. Rivera
Objective covered: Objective 4 — Apply basic probability rules, including conditional probability.

How to use this page

Everything here is a link to an external resource — open it in your browser, the same way you'd open a YouTube link. Nothing needs to be downloaded.

This week's load is deliberately light: ~4 short readings + ~3 short videos, grouped by the four ideas from the lecture. Read or watch one item per group and you're ready for the quiz; do all of them and you'll be very comfortable. Total time is roughly 45–55 minutes if you do everything, far less if you pick one per group.

Reading order that matches the lecture: ① sample spaces, events & basic probability → ② complement & addition rule → ③ multiplication & independence → ④ conditional probability (and the base-rate trap).

A habit to start now: before you compute any probability, you already know the move from class — list the whole sample space first, then count favorable over total. And whenever new information appears, ask the conditional question: given what I now know, what changed?

① Sample Spaces, Events & Basic Probability

Maps to Lecture Segment 2. The hard part of any probability problem is writing the sample space correctly — once the list is right, the answer is division.

Reading — "Probability: the basics" (Khan Academy, article)
🔗 https://www.khanacademy.org/math/statistics-probability/probability-library/basic-theoretical-probability/a/probability-the-basics
Why it's assigned: the cleanest plain-language version of favorable ÷ total, with the two iron rules we drew on the board — every probability sits between 0 and 1, and the whole sample space sums to 1.
⏱ ~6 min

Video — "Sample spaces for compound events" (Khan Academy)
🔗 https://www.khanacademy.org/math/statistics-probability/probability-library/multiplication-rule-independent/v/compound-sample-spaces
Why it earns the click: a quick worked example of listing every outcome before computing — exactly the coin-flipped-twice move from Segment 2, shown as a table and a list.
⏱ ~5 min

② Complement & the Addition Rule (the "OR" rule)

Maps to Lecture Segment 3. Two hooks: "at least one" = 1 minus "none" (the complement), and OR means add — but subtract the overlap unless the events can't coexist.

Reading — "Addition rule for probability (basic)" (Khan Academy, article)
🔗 https://www.khanacademy.org/math/statistics-probability/probability-library/addition-rule-lib/a/addition-rule-for-probability-basic
Why it's assigned: nails the exact distinction from class — mutually exclusive events (just add) vs. events that overlap (add, then subtract P(A and B)) — the King-or-Heart trap that gives 16/52, not 17/52.
⏱ ~6 min

③ The Multiplication Rule & Independence (the "AND" rule)

Maps to Lecture Segment 5. The lesson that sticks: AND means multiply — but only when the events are independent. If one outcome nudges the other, you can't just multiply.

Reading — "The general multiplication rule" (Khan Academy, article)
🔗 https://www.khanacademy.org/math/statistics-probability/probability-library/multiplication-rule-independent/a/general-multiplication-rule
Why it's assigned: shows when P(A and B) = P(A) × P(B) is allowed (independent events) and what to do when it isn't — the difference between drawing a card with vs. without replacement, straight from Segment 5.
⏱ ~7 min

Video — "Probability Part 1: Rules and Patterns — Crash Course Statistics #13"
🔗 https://www.youtube.com/watch?v=OyddY7DlV58
Why it earns the click: the liveliest tour of the AND and OR rules together, with the gambler's-fallacy "no memory" idea from the hook shown in action.
⏱ ~12 min

④ Conditional Probability (and the Base-Rate Trap)

Maps to Lecture Segments 6–7. The line to carry out of this week: "given" shrinks the world to one row — and P(A | B) is not P(B | A), which is exactly why a "99% accurate" positive test can still mean only a ~17% chance of disease.

Reading — "Conditional probability and independence" (Khan Academy, article)
🔗 https://www.khanacademy.org/math/statistics-probability/probability-library/conditional-probability-independence/a/conditional-probability-and-independence
Why it's assigned: defines P(A | B) the way we did on the two-way table — of the times B happened, how often did A? — and then uses it as the real independence test (is P(A | B) = P(A)?), tying Segments 6 and 7 together.
⏱ ~7 min

Video — "Probability Part 2: Updating Your Beliefs with Bayes — Crash Course Statistics #14"
🔗 https://www.youtube.com/watch?v=oZCskBpHWyk
Why it earns the click: the clearest short take on updating a probability when new information arrives — the medical-test / base-rate idea from Segment 7, shown with natural frequencies so the "~17%, not 99%" result feels obvious.
⏱ ~13 min

Optional one-stop reference (free online text)

If you'd like one optional reference to skim all term, OpenIntro Statistics keeps its full text and per-section videos free to read online. Chapter 3 ("Probability") covers everything in this week — defining probability, the addition and multiplication rules, and conditional probability (including probability trees).
🔗 https://www.openintro.org/book/os/
Why it's here: a reputable, currently-available reference you can return to in later weeks — entirely optional this week.

Pick-one quick path (≈15 min total)

In a hurry? Do exactly these four and you'll be ready for the quiz:
1. Read Probability: the basics (group ①).
2. Read Addition rule for probability (basic) (group ②).
3. Read The general multiplication rule (group ③).
4. Watch Crash Course #14 — Updating Your Beliefs with Bayes (group ④).

Heads-up (links rot): these point to outside sites that occasionally move or rename pages. If a link ever fails, tell Prof. Rivera and use the OpenIntro reference above in the meantime.