Lesson M3

M3 Modelling with probability Quiz: AQA Maths, Unit 11

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

In partnership with Revision Ninja

Lesson M3, Modelling with probability: 20 multiple choice questions for the AQA Maths (7357), Unit 11: Statistics, written with Revision Ninja.

Host it live on the board and students join with a game code on their own devices, or revise alone with Free Play. The answers are revealed in the game.

Host this setFree Play

The 20 questions

  1. Why are simplifying assumptions stated when constructing a mathematical probability model?

    • Define valid conditions
    • Remove all uncertainty
    • Guarantee exact accuracy
    • Increase sample size

  2. Which real-world customer behaviour violates the assumption of independent arrivals in a model?

    • Arriving in groups
    • Arriving at noon
    • Paying by card
    • Arriving on foot

  3. Which real-world property violates the model assumption that a coin is fair?

    • Two outcomes
    • Independent tosses
    • Fixed trials
    • Coin bias

  4. In manufacturing, which phenomenon causes defective items in a batch to violate independence assumptions?

    • Machine fault clustering
    • Constant temperature
    • Uniform inspection
    • Random raw materials

  5. Which condition is required for a binomial probability distribution model to be valid?

    • Independent trials
    • Variable probability
    • Continuous outcomes
    • Unlimited trials

  6. A model says P(rain on any day) = 0.3, independently each day. What is the probability of rain on both Monday and Tuesday?

    • 0.60
    • 0.06
    • 0.09
    • 0.30

  7. Under the same model (P(rain) = 0.3 each day, independent), what is the probability of rain on at least one of Monday, Tuesday and Wednesday?

    • 0.900
    • 0.027
    • 0.343
    • 0.657

  8. Real weather has positive day-to-day correlation. An independent model estimates consecutive rain probability as:

    • Too high
    • Too low
    • Unchanged
    • Exactly zero

  9. Which condition must hold for P(A intersection B) = P(A) * P(B) to apply?

    • Mutually exclusive events
    • Independent events
    • Exhaustive events
    • Dependent events

  10. What is a key practical limitation of computer-generated random numbers in probability simulations?

    • They are continuous
    • They are pseudo-random
    • They are symmetrical
    • They are skewed

  11. A model uses P(A) = 0.5 and P(B) = 0.4 with A and B independent. What is the probability that neither occurs?

    • 0.10
    • 0.20
    • 0.70
    • 0.30

  12. How is a theoretical probability model primarily evaluated against real-world situations?

    • Comparing observed frequencies
    • Calculating the mean
    • Assuming independence
    • Increasing trial numbers

  13. A fair die is rolled twice. What is the probability of exactly one six?

    • 11/36
    • 1/3
    • 5/18
    • 1/6

  14. Adding more realistic detail to a mathematical model involves balancing accuracy against which factor?

    • Simplicity
    • Significance
    • Independence
    • Variance

  15. A stock price is modelled to rise each day with probability 0.6, independently. What is the probability it rises on exactly 2 of 3 days?

    • 0.648
    • 0.288
    • 0.432
    • 0.216

  16. If P(A) = 0.3 and P(B) = 0.2, what is P(A ∩ B) under independence?

    • 0.15
    • 0.50
    • 0.10
    • 0.06

  17. How can a probability model assuming a constant call arrival rate be improved?

    • Use a Normal distribution
    • Ignore peak hours
    • Assume zero variance
    • Vary rate by time

  18. If defects cluster rather than occur independently, how does the proportion of defective batches change?

    • It stays constant
    • It increases
    • It decreases
    • It doubles

  19. P(A) = 0.2 and P(B) = 0.5 with A and B independent. Let C be the event that A or B occurs. What is P(C)?

    • 0.50
    • 0.70
    • 0.10
    • 0.60

  20. Four independent tests each succeed with probability 0.8. What is the probability all four succeed?

    • 0.2048
    • 0.4096
    • 0.3200
    • 0.8000

All AQA Maths quizzes