Grade 3 Probability Quiz — 45 minutes (Total: 75 points)
Instructions (printable)
- Time: 45 minutes. Total points: 75.
- Show all work in the spaces provided. Use drawings or lists when helpful.
- Write answers clearly. For explanation items, use complete sentences.
- This quiz includes short answers, reasoning items, and two items marked for peer feedback. Use the peer-feedback rubric at the end for those items.
- No calculators needed.
Questions (15 questions — each worth 5 points)
(5 pts — Concept first / Explicit model) A spinner is divided into 4 equal sections labeled Red, Blue, Yellow, and Green. The teacher models probability this way: Probability of Red = number of red sections ÷ total sections = 1 ÷ 4 = 1/4.
- a) Write the probability of landing on Blue as a fraction.
- b) Explain in 1–2 sentences why that fraction shows the chance of Blue using unit reasoning and quantity relationships.
(5 pts) A bag contains 6 marbles: 3 red, 2 blue, and 1 yellow.
- a) What is the probability of picking a red marble on one random draw? Write as a fraction.
- b) Is picking a red marble likely, unlikely, certain, or impossible? Write the word and one-sentence justification.
(5 pts — Experimental inquiry) A spinner with 3 equal sections labeled A, B, and C was spun 20 times. Results: A — 8 spins, B — 7 spins, C — 5 spins.
- a) Write the experimental probability for each outcome (A, B, C) as fractions.
- b) Compare the experimental probabilities to the theoretical probability 1/3. In one sentence say which outcome from the experiment seems closest to the theoretical probability and why.
(5 pts) Toss a coin twice. List the complete set of possible outcomes (sample space). Then give the probability (as a fraction) of getting exactly one head.
(5 pts — True / False with reasoning) Statement: "If an event is impossible, its probability is 1."
- Write True or False, then give a one-sentence explanation using correct probability language (certain, impossible, etc.).
(5 pts — Community scenario; collaborative casework) At the school fair a spin wheel has 5 equal parts. One part wins a small prize and the other four parts do not win.
- a) If one student spins once, what is the probability they win? (fraction)
- b) Two different students each spin once. Show work and write the probability that at least one of the two students wins. Explain your method (you may use a list, table, or a short sentence).
(5 pts — Equivalence) Circle the pair(s) that are equivalent probabilities and explain in one sentence why:
- A: 2/4
- B: 1/2
- C: 4/8
- D: 1/3 (State which letters are equivalent and give the short explanation.)
(5 pts — Mini-inquiry) A spinner has 6 equal sections: 3 green, 2 red, and 1 blue.
- a) Without drawing, which color is most likely? Write the color and the probability as a fraction.
- b) Explain in 1 sentence how you used composition/decomposition of the sections to find the probability.
(5 pts — Coached practice) A bag contains 10 marbles. The probability of picking a yellow marble at random is 3/10.
- How many yellow marbles are in the bag? Show the short calculation that matches the fraction to the count.
(5 pts — Community counting) On a neighborhood walk you count 12 houses. Three of the 12 houses have a compost bin in the front yard.
- a) If you choose one house at random, what is the probability it has a compost bin? Write as a fraction and a word (e.g., likely/unlikely).
- b) Explain how the fraction shows the relationship between the part (houses with compost bins) and the whole (total houses).
(5 pts — Vocabulary matching) Match each probability word to its best meaning. Write the letter of the meaning next to the word. Words:
- A: certain
- B: impossible
- C: likely
- D: unlikely
- E: equally likely Meanings:
- Cannot happen
- Happens every time
- About the same chance as not happening
- Probably will happen
- Probably will not happen
(5 pts — Complement) A prize wheel has 10 equal sections: 4 blue, 3 yellow, 2 green, 1 red.
- a) What is the probability of landing on blue? (fraction)
- b) What is the probability of not landing on blue? (fraction, simplified)
(5 pts — Experimental vs theoretical reasoning) A student flipped a fair coin 30 times and got 18 heads.
- a) What is the experimental probability of heads from this experiment? (fraction)
- b) The theoretical probability of heads is 1/2. Explain in 1–2 sentences whether the experimental result is close to the theoretical result and why.
(5 pts — Composition & decomposition with numbers) Choose one card at random from six numbered cards: 1, 2, 3, 4, 5, 6.
- a) What is the probability of picking an even number? (fraction)
- b) If you pick an even number, list those even numbers and then give the probability that the number is greater than 3 among those evens.
(5 pts — Create & explain; peer-feedback target) Design a spinner with 8 equal parts using items from your community (for example: apple, bike, tree, bus, dog, cat, mailbox, bench). Write which item is your favorite and:
- a) State the probability (fraction) of the spinner landing on your favorite.
- b) In 1–2 sentences explain why this fraction, and show an equivalent fraction using decomposition or composition (for example, show how 4/8 is the same as 1/2). (This question is marked for peer feedback — use the peer-feedback rubric below.)
Peer-feedback rubric (use for Questions 3, 6, and 15)
- Score 3 — Excellent explanation
- Correct answer and clear reasoning.
- Uses counts or fractions accurately and links to the model (spinner, list, or experiment).
- Explanation uses at least one mastery thread term (unit, part/whole, equivalent, compose/decompose).
- Score 2 — Partial explanation
- Correct answer but explanation is missing some reasoning or has a small error.
- Shows counts or fractions but does not fully connect to the model words.
- Score 1 — Needs improvement
- Incorrect answer or explanation shows misunderstanding (counts wrong or uses probability words incorrectly).
Label peer feedback with the rubric score (3/2/1) and a one-sentence suggestion.
Answer Key and Scoring Guide (detailed explanations)
Each question worth 5 points. Rubric gives point distribution often as: Correct answer and clear explanation = 5; correct answer with minimal explanation = 3–4; partial work or incorrect answer with reasoning = 1–2; blank or no work = 0. Detailed solutions below.
Answer:
- a) 1/4.
- b) Explanation: There is 1 blue section out of 4 equal sections, so 1 ÷ 4 = 1/4. Scoring (5 pts): 3 pts for correct fraction, 2 pts for explanation referencing "1 out of 4" or unit reasoning.
Answer:
- a) Probability red = 3/6 = 1/2 (can simplify to 1/2).
- b) Likely. Explanation: Half the marbles are red (3 out of 6), so getting red is likely. Scoring: 3 pts for correct fraction (simplified), 2 pts for correct word and justification.
Answer:
- a) Experimental probabilities: A = 8/20 = 2/5; B = 7/20; C = 5/20 = 1/4.
- b) Theoretical probability for each is 1/3 ≈ 6.67/20. A (2/5 = 8/20) is closest to 1/3 because 8/20 is closer to 6.67/20 than 7/20 or 5/20; or say A has the closest count to the expected 20/3 ≈ 6.7. Scoring: 2 points per correct experimental fraction (up to 4), 1 point for correct comparative sentence (explain closeness).
Peer-feedback: Use rubric.
Answer:
- Sample space: HH, HT, TH, TT (list of 4 outcomes).
- Exactly one head outcomes: HT and TH → 2 out of 4 → probability = 2/4 = 1/2. Scoring: 3 pts for full sample space, 2 pts for correct probability and simplification.
Answer:
- False. Explanation: An impossible event has probability 0, while a certain event has probability 1. Scoring: 3 pts for correct True/False, 2 pts for explanation using 0 and 1 and correct terminology.
Answer:
- a) Single spin win probability = 1/5.
- b) Two students each spin once. Probability at least one wins = 1 − P(both lose). P(a student loses) = 4/5. P(both lose) = (4/5) × (4/5) = 16/25. So probability at least one wins = 1 − 16/25 = 9/25. Alternate listing method: list outcomes (win/lose pairs) and count favorable pairs (but complement is shorter). Scoring: 2 pts for part (a), 3 pts for part (b): 2 pts for correct complement setup and calculation, 1 pt for clear explanation or alternate correct listing.
Peer-feedback: Use rubric.
Answer:
- Equivalent pairs: A (2/4), B (1/2), and C (4/8) are equivalent because they all simplify or convert to 1/2. D (1/3) is not equivalent.
- Short explanation: 2/4 = 1/2 and 4/8 = 1/2 so they represent the same part/whole relationship. Scoring: 3 pts for identifying letters A, B, C as equivalent, 2 pts for correct explanation.
Answer:
- a) Most likely color: Green. Probability = 3/6 = 1/2.
- b) Explanation: There are 3 green parts out of 6 total parts; composing the 6 parts and decomposing the 3 favorable shows 3 ÷ 6 = 1/2. Scoring: 3 pts for correct probability and color, 2 pts for explanation using compose/decompose language or correct reasoning.
Answer:
- There are 3 yellow marbles. Explanation: Probability 3/10 means 3 out of 10 marbles are yellow, so count = 3. Scoring: 3 pts for correct count (3), 2 pts for showing relation 3/10 and explanation.
Answer:
- a) Probability = 3/12 = 1/4. Word: unlikely (or "not likely") — teacher may accept "unlikely" with reasoning.
- b) Explanation: 3 is the part (houses with compost bins) and 12 is the whole (total houses), so part/whole = 3/12 = 1/4. Scoring: 3 pts for correct fraction (simplified), 2 pts for correct word and explanation linking part/whole.
Answer (matching):
- A: certain → 2. Happens every time
- B: impossible → 1. Cannot happen
- C: likely → 4. Probably will happen
- D: unlikely → 5. Probably will not happen
- E: equally likely → 3. About the same chance as not happening Scoring: 1 point per correct match (5 total).
Answer:
- a) Probability blue = 4/10 = 2/5.
- b) Probability not blue = 1 − 2/5 = 3/5 (or compute remaining counts: 3+2+1 = 6/10 = 3/5). Scoring: 3 pts for part (a) (correct reduced fraction), 2 pts for part (b) correct complement and simplification.
Answer:
- a) Experimental probability = 18/30 = 3/5.
- b) Theoretical probability is 1/2 = 0.5. Experimental 3/5 = 0.6. This is somewhat close but not exact; with 30 trials some variation is expected, so 18 heads is a reasonable result though slightly above the theoretical value. Scoring: 3 pts for correct fraction, 2 pts for explanation comparing 0.6 to 0.5 and noting variation in experiments.
Answer:
- a) Even numbers among 1–6: 2, 4, 6 → 3 favorable out of 6 → probability = 3/6 = 1/2.
- b) Evens are {2, 4, 6}. Among these evens, numbers greater than 3 are {4, 6} → 2 out of 3 evens → probability = 2/3. Scoring: 3 pts for part (a) correct fraction and simplification, 2 pts for part (b) correct listing and fraction.
Answer (sample model and rubric scoring):
- a) Example student answer: If spinner parts are Apple, Bike, Tree, Bus, Dog, Cat, Mailbox, Bench and favorite = Bike, probability = 1/8.
- b) Explanation: There is 1 Bike part out of 8 equal parts so 1/8. An equivalent fraction by composition: 2/16 or by decomposition if I grouped 2 parts as "transport" and showed 1/8 = 2/16 (students may show an equivalent like 4/32, or decompose as 1/8 = (1 ÷ 8)). To show a clear equivalence using composition, a student might show 1/8 = 2/16 and explain both represent the same part/whole. Scoring: 3 pts for correct fraction and naming favorite, 2 pts for an explanation showing an equivalent fraction and linking to part/whole. Peer-feedback: Use rubric. Expect a peer score (3/2/1) and a one-sentence suggestion.
End of exam.