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Probability Models and Long-Run Frequency — 7th Math: Statistics & Probability practice questions

26 multiple-choice questions and 5 flashcards on Probability Models and Long-Run Frequency, about 17% of the 7th Math: Statistics & Probability bank. Every one carries a written rationale.

Written and maintained by Nick Burton · last updated 2026-08-22 · how we write and review questions

What this chapter covers

Probability Models and Long-Run Frequency is one of 5 chapters in CoStudy's 7th Math: Statistics & Probability bank, and it holds 26 of the bank's 150 multiple-choice questions — roughly 17% of the total. That proportion is not arbitrary: chapters follow the certifying body's published exam outline, and the number of questions in each is set by that domain's published weight, so the share of your practice time this chapter takes matches the share of the real exam it accounts for.

Studying by chapter is worth doing once you have a diagnostic score. A single overall percentage tells you whether you are close; it does not tell you which domain is dragging. Working a weak chapter in isolation, and re-testing it in isolation, is the fastest way to move a score that has stalled — and it is why the mock exams in CoStudy report by domain rather than as one number.

Free Probability Models and Long-Run Frequency practice questions

10 questions drawn from this chapter, with the full rationale shown — the controlling principle behind the right answer, and why each wrong option tempts and fails.

A survey of 100 people finds 45 prefer apples. Expected number preferring apples in a town of 2,000:

  1. 450
  2. 900
  3. 45
  4. 1,000

Answer: B — 900

45/100 × 2,000 = 900. (A) multiplied by 10 instead of 20; (C) raw sample count; (D) assumed 50%.

You spin a spinner and record outcomes: A 30, B 10, C 10. The probability model is BEST described as:

  1. Uniform with P = 1/3 for each
  2. Non-uniform — P(A) ≈ 3/5, P(B) ≈ 1/5, P(C) ≈ 1/5
  3. Theoretical 1/2 each
  4. Impossible — counts don't sum to 100

Answer: B — Non-uniform — P(A) ≈ 3/5, P(B) ≈ 1/5, P(C) ≈ 1/5

Observed frequencies are uneven, so a non-uniform model fits: 30/50, 10/50, 10/50. (A) ignores data; (C) makes no sense; (D) counts sum to 50, fine.

Events A and B are independent. P(A) = 1/2, P(B) = 1/3. P(A and B) =

  1. 5/6
  2. 1/6
  3. 1/5
  4. 2/3

Answer: B — 1/6

P(A and B) = P(A) × P(B) = (1/2)(1/3) = 1/6 for independent events. (A) P(A or B) for mutually exclusive; (C) wrong; (D) P(A) × P(B) error.

A 4-section spinner has P(red) = 0.4, P(blue) = 0.3, P(green) = 0.2. P(yellow), the remaining color?

  1. 0.1
  2. 0.5
  3. 0.9
  4. Cannot be determined

Answer: A — 0.1

All probabilities sum to 1: 1 − (0.4 + 0.3 + 0.2) = 0.1. (B/C) arithmetic errors; (D) it CAN be determined.

An event has P = 0.25. This event is:

  1. Certain
  2. Impossible
  3. Unlikely but possible
  4. Very likely

Answer: C — Unlikely but possible

P = 0.25 = 25% chance. Less than 50%, so unlikely but clearly possible. (A) P = 1; (B) P = 0; (D) would be P close to 1.

P(rolling an even number on a standard die):

  1. 1/6
  2. 1/3
  3. 1/2
  4. 2/3

Answer: C — 1/2

Even numbers: {2, 4, 6} = 3 out of 6 = 1/2. (A) one outcome; (B) two outcomes; (D) four outcomes.

Two data sets: Set A mean = 70, MAD = 2; Set B mean = 70, MAD = 8. Which has more consistent values?

  1. Set A — smaller MAD means values cluster closer to the mean
  2. Set B — larger MAD means values are closer to the mean
  3. They are equally consistent
  4. Cannot determine without the raw data

Answer: A — Set A — smaller MAD means values cluster closer to the mean

Smaller MAD = values are more tightly clustered around the mean = more consistent. (B) reverses the interpretation; (C) they have different MADs; (D) MAD directly indicates consistency.

To estimate the probability of an event using a computer simulation:

  1. Run the simulation once
  2. Calculate the theoretical value
  3. Run many trials and use the experimental relative frequency
  4. Guess randomly

Answer: C — Run many trials and use the experimental relative frequency

C) Law of large numbers: many trials approximate the true probability. A) One trial gives noisy results. B) Bypasses simulation. D) Off-task.

In comparing two data distributions, a larger MAD indicates:

  1. A higher mean
  2. Greater spread (variability) around the mean
  3. A larger median
  4. More data points

Answer: B — Greater spread (variability) around the mean

MAD measures average spread; larger MAD = more variability. (A/C) relate to center, not spread; (D) MAD is about distance, not count.

The THEORETICAL probability of flipping heads is 1/2. If you flip 100 times and get 47 heads, the EXPERIMENTAL probability is:

  1. 1/2
  2. 0
  3. 47/100
  4. 100/47

Answer: C — 47/100

C) Observed successes / trials. A) Theoretical, not experimental. B) Not zero. D) Inverted.

Probability Models and Long-Run Frequency flashcards

4 cards from the 5 in this chapter.

Compare two distributions by comparing?

Centers, spreads, and shapes.

Two data sets with the same mean — what else compares them?

Their spread (MAD, range, or IQR).

Mean absolute deviation in one sentence?

Average distance of each value from the mean.

Complement rule?

P(not A) = 1 − P(A).

Practise the full chapter

These are a sample. The full Probability Models and Long-Run Frequency chapter runs 31 items with per-chapter progress tracking, on the web and in the iOS app.

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