Week 5 — Quiz (auto-graded) · Probability Foundations

Course: Introduction to Statistics (18-week generic edition)
Objective tested: Objective 4 — probability rules and conditional probability (the week's portion of the objective).
Points: 10 (1 each) · Assignment group: Quizzes (15% of grade) · Due: end of Week 5 · Closed to AI.

This is the human-readable quiz with its vetted answer key and feedback. The import-ready Classic QTI is in F-quiz-week-05-qti.xml; the reusable item-bank entries and the Canvas placement block are at the bottom of this file.

Blueprint

No trick questions; distractors target the Week 5 misconceptions named in the lecture outline.

Questions, key, and feedback

Q1 (MC). An arcade prize wheel is designed so that P(landing on GOLD) = 0.05. Which statement best interprets this probability?
- A. Exactly 1 out of every 20 spins will land on gold
- B. In a very large number of spins, about 5% will land on gold ✅
- C. The next 20 spins are guaranteed to include at least one gold
- D. Gold becomes impossible for a while after each gold result
Feedback: Probability is a long-run relative frequency — a promise about the long run, silent about any short stretch. (A is the "exactly one in six rolls" misread; C and D promise things about specific spins.)

Q2 (MC). You roll two fair six-sided dice. What is the probability the sum is 11?
- A. 1/18 ✅
- B. 1/36
- C. 2/11
- D. 1/12
Feedback: The sample space has 36 equally likely pairs; a sum of 11 happens 2 ways — (5,6) and (6,5) — so 2/36 = 1/18. (1/36 forgets the second ordering; 2/11 divides by the number of possible sums, which are not equally likely.)

Q3 (MC). A skateboard factory's final inspection passes 94% of the decks it tests and fails the rest. What is the probability a randomly chosen deck fails inspection?
- A. 0.94
- B. 0.50
- C. 1.06
- D. 0.06 ✅
Feedback: Complement rule: P(fail) = 1 − P(pass) = 1 − 0.94 = 0.06. (B is the "it either passes or it doesn't, so 50/50" trap — two outcomes are not automatically equally likely; C added instead of subtracting and escaped the 0-to-1 scale.)

Q4 (MC). One card is drawn from a standard 52-card deck. What is P(queen or club)?
- A. 17/52
- B. 13/52
- C. 16/52 ✅
- D. 1/52
Feedback: General addition rule: 4/52 + 13/52 − 1/52 (the queen of clubs was counted twice) = 16/52. (17/52 forgets to subtract the overlap; 13/52 counts only clubs; 1/52 is the overlap itself.)

Q5 (Multiple answer — select all that apply). Which pairs of events are disjoint (mutually exclusive)?
- A. One card is drawn: "it is a heart" and "it is a jack"
- B. One card is drawn: "it is a seven" and "it is a king" ✅
- C. A spinner is spun once (it lands on exactly one sector): "it lands on red" and "it lands on blue" ✅
- D. One die is rolled: "it shows an even number" and "it shows a 6"
- E. One die is rolled: "it shows an even number" and "it shows a 3" ✅
Feedback: Disjoint = the two events cannot both happen on that one trial. A card can be the jack of hearts (A overlaps); a 6 is even (D overlaps). One card can't hold two ranks, one spin lands one color, and 3 isn't even — B, C, E can't co-occur.

Q6 (Matching). Match each rule to its formula.
| Rule | Correct formula |
|---|---|
| Complement rule | P(not A) = 1 − P(A) |
| Addition rule for disjoint events | P(A or B) = P(A) + P(B) |
| General addition rule | P(A or B) = P(A) + P(B) − P(A and B) |
| Multiplication rule for independent events | P(A and B) = P(A) × P(B) |
Feedback: NOT subtracts from 1; OR adds (subtracting any overlap); AND multiplies — but only when the events are independent.

Q7 (MC). A spinner lands on purple with probability 0.2 on any spin, and spins are independent. What is the probability that both of two spins land on purple?
- A. 0.04 ✅
- B. 0.40
- C. 0.20
- D. 0.02
Feedback: Independent events: P(purple and purple) = 0.2 × 0.2 = 0.04. (0.40 added instead of multiplying — "and" shrinks, it doesn't grow; 0.20 treats two demands as one.)

Q8 (True / False). A fair die has gone 20 rolls without showing a 4. "A 4 is now more likely on the next roll, because results must even out."
- True
- False ✅
Feedback: False — the gambler's fallacy. Rolls are independent; the die has no memory, so P(4) = 1/6 on every roll. The long run evens out proportions by swamping early gaps, not by compensating for them.

Q9 (MC). A lamp factory's one-day quality log covers 200 bulbs: the day shift made 150 bulbs, 6 defective; the night shift made 50 bulbs, 6 defective. What is P(defective | night shift)?
- A. 0.06
- B. 0.12 ✅
- C. 0.50
- D. 0.25
Feedback: "Given night shift" shrinks the world to the night shift's 50 bulbs: 6/50 = 0.12. (0.06 is the overall rate 12/200; 0.50 is the swapped direction P(night | defective) = 6/12; 0.25 is P(night shift) = 50/200. Note both shifts had 6 defectives — but very different rates: 6/150 = 0.04 vs. 6/50 = 0.12. Counts aren't rates.)

Q10 (MC). Same lamp-factory log (day shift: 6 defective of 150; night shift: 6 defective of 50). A defective bulb has just turned up in the reject bin. Which probability answers the question "how likely is it that this bulb came from the night shift?"
- A. P(defective | night shift) = 0.12
- B. P(night shift) = 0.25
- C. P(defective and night shift) = 0.03
- D. P(night shift | defective) = 0.50 ✅
Feedback: The "given" here is what you already know — the bulb is defective — so the world shrinks to the 12 defectives, 6 of which are the night shift's: 6/12 = 0.50. Swapping the bar (option A) answers a different question about the night shift's own output.

Answer key (quick reference)

Quality gate (self-checked): each single-answer item has exactly one correct option; the multiple-answer item's three disjoint pairs are the only disjoint pairs listed (heart/jack and even/6 genuinely overlap); every computed value re-verified in the week's math script (2/36 = 1/18; 1 − 0.94 = 0.06; 4 + 13 − 1 = 16 clubs/queens; 0.2² = 0.04; 6/50 = 0.12; 6/12 = 0.50; 12/200 = 0.06; 50/200 = 0.25; 6/200 = 0.03); no positional pattern in the MC key (B A D C · A · B D) and no length giveaway (options within each item are comparable lengths); every item answerable from its text alone (no table images); no item asserts a fact outside the Week 5 course definitions; no scenario reuses the tutorial, practice, chapter, lab, or assignment surfaces (arcade wheel, two-dice sum 11, skateboard decks, queen-or-club, and the lamp-factory shifts appear only here).

Item-bank entries (for variants + the midterm/final)

All ten items are tagged week=5 · objective=4 · topic=probability-foundations and deposited in Item Bank: Week 5 — Probability Foundations with idents w05q1–w05q10. The midterm (Week 9), the final (Week 18), and per-term variant updates draw fresh variants from this bank's concepts — never these live stems. (Tags: w05q1 long-run-meaning, w05q2 sample-space, w05q3 complement, w05q4 general-addition, w05q5 disjoint-recognition, w05q6 rule-formulas, w05q7 multiplication-independence, w05q8 gamblers-fallacy, w05q9 conditional-table, w05q10 conditional-direction.)

Canvas placement block

canvas_object    = Quizzes::Quiz
title            = "Week 5 Quiz — Probability Foundations"
assignment_group = "Quizzes"
points_possible  = 10
grading_type     = points
due_offset_days  = 6        # end of the module's week
published        = true
shuffle_answers  = true