Lesson P5

P5 Empirical probability and sample size Quiz: AQA Maths, Unit 5

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson P5, Empirical probability and sample size: 20 multiple choice questions for the AQA GCSE Maths (8300), Unit 5: Probability, written with Revision Ninja.

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The 20 questions

  1. Which term describes probability calculated from the results of an experiment?

    • Relative frequency
    • Conditional probability
    • Subjective probability
    • Theoretical probability

  2. As the number of trials increases, what does empirical probability approach?

    • Sample mean
    • Theoretical probability
    • One
    • Zero

  3. Why must a sample be unbiased when estimating an empirical probability?

    • Increase sample size
    • Reflect true probability
    • Guarantee certainty
    • Ensure equal trials

  4. Which sample size gives the most reliable estimate of an empirical probability?

    • Larger sample
    • Ten trials
    • Single trial
    • Smaller sample

  5. An experiment is repeated 10 times and gives 7 successes. What is the empirical probability of success?

    • 0.07
    • 0.7
    • 7
    • 0.3

  6. A fair coin is tossed 4 times and lands heads every time. What is the empirical probability of heads?

    • 0
    • 0.5
    • 1
    • 0.25

  7. What is a disadvantage of using a small sample size to estimate probability?

    • Fixed theoretical probability
    • Zero relative frequency
    • Biased outcomes only
    • High chance variation

  8. A fair coin has theoretical probability 0.5 of heads. Which empirical result from 1000 tosses is most likely to be close to this?

    • 0.9
    • 0.2
    • 0.1
    • 0.48

  9. A biased dice is rolled 200 times and shows a 3 on 50 rolls. What is the empirical probability of a 3?

    • 1/5
    • 1/3
    • 1/2
    • 1/4

  10. A drawing pin lands point up 34 times in 100 throws. What is the empirical probability of point up?

    • 0.66
    • 0.34
    • 0.5
    • 0.034

  11. A survey of 60 people finds 15 chose option X. What is the empirical probability of choosing X?

    • 0.75
    • 0.25
    • 0.15
    • 0.4

  12. A spinner is spun 250 times and lands red 75 times. Which value best estimates the probability of red?

    • 0.03
    • 0.25
    • 0.3
    • 0.75

  13. A coin is tossed 500 times. The empirical probability of heads is 0.43 and the theoretical probability is 0.4. How many more heads occurred than the theory predicts?

    • 200
    • 15
    • 25
    • 215

  14. An empirical probability from 40 trials is 0.6. How many times did the outcome occur?

    • 40
    • 60
    • 24
    • 6

  15. A survey of 80 people found 20 owned a car. What is the empirical probability of owning a car?

    • 0.2
    • 0.25
    • 0.75
    • 0.4

  16. Which number of coin tosses gives the most reliable estimate of obtaining heads?

    • 100 tosses
    • 50 tosses
    • 10 tosses
    • 1000 tosses

  17. (H) A coin is tossed 200 times and gives 0.46 as the empirical probability of heads. How many heads were there?

    • 92
    • 108
    • 46
    • 98

  18. Sample X uses 100 trials and Sample Y uses 300 trials. Which is more reliable?

    • Both equally
    • Sample X
    • Sample Y
    • Neither sample

  19. (H) An empirical probability from 600 trials is 0.3, while the theoretical probability is 1/3. What is the difference between the two?

    • 0.333
    • 0.1
    • 0.3
    • 0.033

  20. What occurs when a sample does not fairly represent the population?

    • Random error
    • Theoretical probability
    • Sample bias
    • High reliability

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