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

Course: Introduction to Statistics (MATH 11) · Silver Oak University (fictional sample) · Prof. Rivera
Objective tested: Objective 4 — apply basic probability rules, including conditional probability (sample spaces; complement; addition; multiplication & independence; conditional probability).
Points: 10 (1 each) · Assignment group: Quizzes (15% of grade) · Due: end of Module 5.

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. All arithmetic is pre-computed and uses friendly numbers.

Questions, key, and feedback

Q1 (MC). You flip a fair coin twice and record the result of each flip in order. How many outcomes are in the sample space?
- A. 2
- B. 4 ✅
- C. 6
- D. 8
Feedback: List it: HH, HT, TH, TT — 4 equally likely outcomes. List the whole space first; the answer follows from the list.

Q2 (MC). For that same experiment (flip a fair coin twice), what is the probability of getting at least one head?
- A. 1/4
- B. 1/2
- C. 3/4 ✅
- D. 1
Feedback: Favorable outcomes are HH, HT, TH (3 of the 4); 3 ÷ 4 = 0.75. Only TT has no head. (Or use the complement: 1 − P(no heads) = 1 − 1/4 = 3/4.)

Q3 (MC). A weather forecast says the probability of rain tomorrow is 0.20. By the complement rule, the probability it does not rain is —
- A. 0.20
- B. 0.80 ✅
- C. 1.20
- D. 0.00
Feedback: P(not A) = 1 − P(A) = 1 − 0.20 = 0.80. An event and its complement must add to 1. (C is impossible — a probability can't exceed 1.)

Q4 (MC). You roll one fair six-sided die. What is the probability of rolling a 2 or a 5? (These can't both happen on one roll.)
- A. 1/6
- B. 1/3 ✅
- C. 1/2
- D. 2/3
Feedback: The two outcomes are mutually exclusive, so just add: 1/6 + 1/6 = 2/6 = 1/3. No overlap to subtract.

Q5 (MC). You draw one card from a standard 52-card deck. What is the probability the card is a King or a Spade?
- A. 17/52
- B. 16/52 ✅
- C. 13/52
- D. 4/52
Feedback: A card can be both (the King of Spades), so subtract the overlap: 4/52 + 13/52 − 1/52 = 16/52 ≈ 0.308. (A = 17/52 is the classic trap — it double-counts the King of Spades.)

Q6 (True / False). A fair coin has landed heads five times in a row. Therefore tails is now more likely than heads on the next flip.
- True
- False ✅
Feedback: False. Independent flips have no memory — the next flip is still 50/50. Believing otherwise is the gambler's fallacy.

Q7 (Multiple answer — select all that apply). For a single trial, which pairs of events are mutually exclusive (they cannot both happen)?
- A. Roll one die: "even number" and "rolling a 3" ✅
- B. Draw one card: "a red card" and "a King"
- C. One coin flip: "heads" and "tails" ✅
- D. One student: "is a freshman" and "is a senior" ✅
- E. Draw one card: "a Heart" and "a face card"
Feedback: Mutually exclusive = no single outcome satisfies both. A (3 is odd, so not even), C, and D can't co-occur. B fails (red Kings exist) and E fails (the J/Q/K of Hearts are both) — those overlap.

Q8 (MC). You roll two fair dice (the rolls are independent). What is the probability that both dice show an even number?
- A. 1/2
- B. 1/4 ✅
- C. 1/3
- D. 1/12
Feedback: Each die is even with probability 3/6 = 1/2; independent events multiply: (1/2) × (1/2) = 1/4. (Independence is what makes multiplying legal here.)

Q9 (MC). A survey of 200 students gives this two-way table:

What is P(owns a car | lives off campus)?
- A. 80/200 = 0.40
- B. 80/100 = 0.80 ✅
- C. 80/110 ≈ 0.73
- D. 110/200 = 0.55
Feedback: "Given off campus" restricts you to the off-campus row (100 students); 80 own a car → 0.80. (A divides by the grand total; C uses the car column — that's P(off campus | owns a car); D is the plain P(owns a car).)

Q10 (Matching). Match each probability rule to its formula.
| Rule | Correct formula |
|---|---|
| Complement rule | P(not A) = 1 − P(A) |
| Addition rule (general) | P(A or B) = P(A) + P(B) − P(A and B) |
| Multiplication rule (independent events) | P(A and B) = P(A) × P(B) |
| Conditional probability | P(A | B) = P(A and B) ÷ P(B) |
Feedback: "OR" subtracts the overlap; "AND" (for independent events) multiplies; "given" divides the joint by P(B); the complement subtracts from 1.

Answer key (quick reference)

Quality gate (self-checked): each single-answer item has exactly one correct option; the multiple-answer item (Q7) lists all three mutually-exclusive pairs and no others; all arithmetic was pre-computed and re-verified (Q1 size 4; Q2 = 3/4; Q3 = 0.80; Q4 = 1/3; Q5 = 16/52; Q8 = 1/4; Q9 = 0.80); no item asserts a fact outside the Week 5 course definitions.

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

All ten items are tagged course=MATH11 · week=5 · objective=4 · topic=probability-foundations and deposited in Item Bank: Week 5 — Probability Foundations. The midterm (Week 8) and the per-term variant updates draw fresh items from this bank. (Tags: q1 sample-space, q2 basic-probability, q3 complement, q4 addition-mutually-exclusive, q5 addition-overlap, q6 gamblers-fallacy, q7 mutually-exclusive-id, q8 multiplication-independence, q9 conditional-probability, q10 probability-rules-formulas.)

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        # 6 days after module start
published       = true
shuffle_answers = true
provenance      = "~ Prof. Rivera's edition · Fall 2026 · built with thecoursemaker.com"