Will we run out of dough on Friday?

Estimate P(sell-out) on a slider, lock it in

• A slider: "on a Friday we prepare 120 dough balls — what is the chance we sell out?" Lock the estimate; the week ends by computing it.
• Reveal: the answer depends on a distribution nobody has yet written down — which is the point of the week.

Complement · union · intersection · conditional · independence (Saylor ch. 3)

• A two-way count of last month's orders: topping (Margherita / other) × neighbourhood (Plainpalais / Eaux-Vives). Every probability in the section is read straight off it.
• Widget: click any cell or margin to see P(A), P(A ∪ B), P(A ∩ B), P(A | B) computed by counting — the exam card "probability from a two-way count" (c3) already exists and seeds this.
• Classify (6 rows): independent or not; mutually exclusive or not — with the "why" for each.

Discrete vs continuous random variables (§4.1)

• Definition: a random variable assigns a number to each outcome. Friday's Margherita count is one; the time the oven takes to heat is another.
• Classify (6 rows): discrete or continuous — sold-out or not, number of tables occupied, weight of dough used, waiting time, number of no-shows, temperature.

Mean and standard deviation of a discrete random variable (§4.2)

• Widget: the distribution of daily Margherita orders, X = 0…5 (per hour), as a bar chart you can reshape by dragging bars — probabilities must sum to 1, and the mean µ = Σ x·P(x) and σ update live.
• Worked example: expected orders per hour → expected dough per Friday, the number the shopping list is built on.
• Exam card c4 ("discrete random variable") is the drill.

n, p, P(X = k), mean np, standard deviation √(npq) (§4.3)

• Widget: binomial bars with sliders for n and p; click a bar for P(X = k), drag a range for P(a ≤ X ≤ b).
• The four conditions (fixed n, two outcomes, constant p, independence) as a checklist the pizzeria situations pass or fail.
• The hook closes: sell-out probability from "each of 140 expected customers orders a Margherita with p = 0.8" — P(X > 120). Exam card c5.

Self-check quiz & where this goes next

• Ten questions: two-way count probabilities, independence, discrete vs continuous, µ and σ of a distribution, binomial P(X = k), np and √(npq), and one "is this binomial?" trap.

Workbook fields, saved for your instructor

• w3_event — a Friday event with its probability, computed from a two-way count you define.
• w3_expected — the expected number of Margheritas per Friday and how you built the distribution.
• w3_binomial — one binomial question about your pizzeria, with n, p and the answer.

The second half of the session

When this week is written, each exercise below becomes a form on this page and a slide in the deck, generated from one array so the two can never disagree — and its solution opens when the instructor reveals it in class. Same engine as Weeks 1–2 (exercises.js).

• Exercise 1 · Probabilities off a two-way count  12 min
  P(A), P(A∪B), P(A∩B), P(A|B) from the orders table
• Exercise 2 · Independent or not?  10 min
  test P(A|B) = P(A) on three pairs of events
• Exercise 3 · Discrete or continuous?  8 min
  six pizzeria variables, classified with a reason
• Exercise 4 · Build a probability distribution  15 min
  orders per hour: the table, and the check that it sums to 1
• Exercise 5 · µ and σ of a random variable  15 min
  Σ x·P(x), then the spread of the order count
• Exercise 6 · Is it binomial?  10 min
  four scenarios against the four conditions
• Exercise 7 · P(X = k) by hand  15 min
  dessert orders: n = 10, p = 0.3, three values of k
• Exercise 8 · The hook closes: P(sell-out)  15 min
  np, √(npq), and the Friday dough decision