Lesson M3

M3 Modelling with probability Quiz: AQA Maths, Unit 11

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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

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The 20 questions

  1. What is the main purpose of stating assumptions when building a probability model?

    • To guarantee the model gives exact real-world predictions
    • To make the model tractable and to show when its conclusions apply
    • To remove the need to compare the model with data
    • To ensure every outcome has equal probability

  2. A model assumes customers arrive independently. Which realistic feature might violate this?

    • Customers having different ages
    • Customers arriving at random times
    • Customers arriving together in groups
    • Customers paying in cash

  3. A model assumes a coin is fair. What is a valid critique?

    • Fair coins always give alternating results
    • The coin may be biased, so P(head) may not equal 0.5
    • Tossing a coin is not a random process
    • Coins can never show heads

  4. A model assumes each item in a batch is defective independently with probability 0.02. Which feature would most increase the true chance of two defects in one batch compared with the model?

    • Items being produced at a constant speed
    • The batch size being fixed in advance
    • Defects occurring in clusters from a single faulty machine setting
    • Each item being checked separately

  5. Which is a limitation of using a binomial model for the number of successes?

    • It requires the mean to equal the variance
    • It works only for continuous data
    • It requires the number of trials to be unknown
    • It assumes trials are independent with a constant probability of success

  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. Weather is in reality correlated from day to day, but the model assumes independence. What effect would this likely have on the probability of several consecutive rainy days?

    • The probability would likely be lower than the independent model predicts
    • The probability would be zero
    • The probability would likely be higher than the independent model predicts
    • The probability would be exactly the same as the independent model predicts

  9. Which assumption makes P(A and B) = P(A) x P(B) valid?

    • A and B are equally likely
    • A and B are mutually exclusive
    • A is a subset of B
    • A and B are independent

  10. A simulation uses a random number generator that is assumed to give independent uniform numbers. What is a practical concern?

    • Uniform numbers cannot be used to model probabilities
    • Simulations require no assumptions to be valid
    • Random numbers are always whole numbers
    • The generator may not be truly random, so results may be biased

  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. Which approach is an appropriate way to critique a probability model?

    • Ignore assumptions that are difficult to test
    • Compare predicted frequencies with observed frequencies from data
    • Assume the model is correct if its probabilities sum to 1
    • Accept the model because it contains a formula

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

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

  14. A model is accurate for predicting outcomes but a teacher argues it should include more realistic detail. Which trade-off does this illustrate?

    • Discrete versus continuous data
    • Hypothesis versus sample evidence
    • Simplicity versus accuracy
    • Accuracy versus rounding

  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. A model gives P(A) = 0.3, P(B) = 0.2 and P(A and B) = 0.1 and is supposed to assume independence. Which critique is valid?

    • The model is consistent with independence since 0.1 is half of 0.2
    • The model is inconsistent with independence since 0.3 x 0.2 = 0.06, not 0.1
    • The model is consistent with independence since 0.1 is less than 0.3 + 0.2
    • The model is consistent since P(A) + P(B) exceeds P(A and B)

  17. A call centre model assumes calls arrive at a constant rate, independently. Which realistic change would most reasonably be suggested?

    • Allow the arrival rate to vary by time of day
    • Assume every date is equally likely for calls
    • Assume exactly one call arrives each hour
    • Assume calls never overlap

  18. If defects cluster in batches, compared with independent defects having the same average rate, the probability that a batch has at least one defect would most likely be:

    • exactly zero
    • higher, because clustering spreads defects evenly
    • unchanged, since the average rate is the same
    • lower, because defects are concentrated in fewer batches

  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

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