Lesson P5

P5 understand that empirical unbiased samples tend towards theoretical probability... Quiz: Pearson Edexcel Maths, Unit 5

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson P5, understand that empirical unbiased samples tend towards theoretical probability...: 20 multiple choice questions for the Pearson Edexcel GCSE Maths (1MA1), Unit 5: Probability, written with Revision Ninja.

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The 20 questions

  1. As sample size increases, relative frequency tends towards what value?

    • Sample mean
    • Zero
    • One
    • Theoretical probability

  2. Why are larger sample sizes more reliable in probability experiments?

    • Outcomes become certain
    • Bias disappears completely
    • Theoretical probability rises
    • Random variation averages out

  3. What defines an unbiased sample?

    • Targeted demographic
    • Fixed numerical quota
    • Largest possible size
    • Equal chance of selection

  4. A fair die is rolled 600 times. What relative frequency for a six is most likely?

    • Close to 1/6, about 0.17
    • Greater than 1
    • Exactly 0
    • About 0.5

  5. Which sample size gives a more reliable estimate of probability?

    • 1000 trials
    • 10 trials
    • 1 trial
    • 5 trials

  6. A sample of 20 students has 8 who like music. What is the estimated proportion for the population, if the sample is unbiased?

    • 0.5
    • 0.4
    • 0.8
    • 0.2

  7. How should you correct a biased survey of only gym members?

    • Use random sampling
    • Double the sample
    • Ask more members
    • Ignore outliers

  8. Which value is closest to 1/6 written as a decimal to 3 decimal places?

    • 0.6
    • 0.167
    • 0.061
    • 1.67

  9. What is the best way to test if a coin is fair?

    • Increase sample size
    • Measure coin mass
    • Throw it once
    • Check coin material

  10. A probability is 0.25. After 40 trials the relative frequency is 0.31. What is the relative frequency most likely to be after 4000 trials?

    • Above 0.5
    • Closer to 0.25
    • Exactly 0.31
    • Exactly 0.25

  11. As the number of trials increases, what happens to relative frequency variation?

    • It increases
    • It decreases
    • It becomes zero
    • It stays constant

  12. Is a poll phoning only landlines considered an unbiased sample?

    • Always accurate
    • Yes
    • No
    • Completely random

  13. What prevents relative frequency from converging on the theoretical probability?

    • Bias in sample selection
    • High number of trials
    • Random variation
    • Large sample size

  14. A spinner has P(red) = 0.6. Which sample size gives a better estimate?

    • 5 spins
    • 10 spins
    • 50 spins
    • 500 spins

  15. Does ten heads in ten coin tosses definitively prove the coin is biased?

    • Statistically impossible
    • No
    • Always true
    • Yes

  16. A random sample of 200 students gives 25% who walk to school. What is the best estimate for the whole school population?

    • 25%
    • 100%
    • 2%
    • 50%

  17. Which die trial is more likely to give a relative frequency close to 1/6?

    • 5 rolls
    • 600 rolls
    • 10 rolls
    • 1 roll

  18. What is the effect of a single unusual result as sample size grows?

    • Zero impact
    • Less impact
    • Total dominance
    • More impact

  19. Why is a survey of 2000 people generally more reliable than one of 50?

    • Larger sample size
    • Less calculation
    • Faster collection
    • Smaller sample size

  20. What does the distribution of results from a large unbiased sample do?

    • Becomes uniform
    • Approximates theoretical distribution
    • Becomes completely random
    • Matches theoretical exactly

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