Lesson P3

P3 Relative expected frequency and theoretical probability Quiz: AQA Maths, Unit 5

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson P3, Relative expected frequency and theoretical probability: 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. How is theoretical probability calculated for equally likely outcomes?

    • Observed frequency divided by number of trials
    • Favourable outcomes divided by total equally likely outcomes
    • Number of outcomes divided by favourable outcomes
    • Number of trials divided by number of outcomes

  2. Probabilities are measured on a scale from which value to which value?

    • -1 to 1
    • 0 to 100
    • 0 to 1
    • 1 to 10

  3. What is the probability of an impossible event?

    • 0
    • 1
    • 0.5
    • -1

  4. What is the probability of a certain event?

    • 0.5
    • 100
    • 1
    • 0

  5. What is the theoretical probability of rolling an even number on a fair six-sided dice?

    • 1/6
    • 1/2
    • 2/3
    • 1/3

  6. A coin has been tossed 100 times. About how many heads are expected if the coin is fair?

    • 25
    • 100
    • 0.5
    • 50

  7. Which description best fits an event with probability 0.1 on the 0 to 1 scale?

    • Certain
    • Unlikely
    • Evens
    • Likely

  8. What percentage corresponds to a theoretical probability of 3/4?

    • 75%
    • 34%
    • 0.75%
    • 25%

  9. A spinner has 8 equal sections, 3 of which are blue. What is the theoretical probability of blue?

    • 3/8
    • 1/3
    • 3/5
    • 5/8

  10. After 1000 coin tosses, the relative frequency of heads is 0.49. What is the theoretical probability of heads for a fair coin?

    • 0.1
    • 0.5
    • 0.49
    • 0.51

  11. A bag holds 5 red, 7 green and 8 blue counters. What is the probability of not drawing a blue counter?

    • 8/20
    • 2/5
    • 7/12
    • 3/5

  12. A fair six-sided dice is rolled. What is the probability of a prime number?

    • 1/2
    • 2/3
    • 1/6
    • 1/3

  13. 500 trials give an outcome 245 times. Compared with its theoretical probability of 1/2, what is true?

    • The relative frequency is exactly equal to it, because 500 trials were done
    • The relative frequency must be exactly 245 out of the 500 trials
    • The relative frequency is slightly less than the theoretical probability
    • The relative frequency is well above 0.6 for this many trials

  14. What is the probability of drawing an ace from a standard 52-card deck?

    • 4/13
    • 1/4
    • 1/52
    • 1/13

  15. A fair six-sided dice is rolled. What is the probability of a number greater than 4?

    • 1/6
    • 1/3
    • 1/2
    • 2/3

  16. A spinner has theoretical probability 0.25 for red. How many reds are expected in 400 spins?

    • 160
    • 100
    • 25
    • 400

  17. (H) A dice is thrown 600 times and a 6 appears 80 times. What is the relative expected frequency of a 6 as a fraction in simplest form?

    • 2/15
    • 1/6
    • 4/15
    • 1/5

  18. (H) A coin's theoretical probability of heads is 0.6, but the relative frequency after 40 tosses is 0.55. What is the best explanation?

    • The coin must be broken, because results should match the theory exactly
    • Small sample sizes can differ from theoretical probability
    • The theoretical probability was wrong and should be recalculated
    • Probability cannot be used for coins at all, only for dice tosses

  19. (H) A bag contains only red and blue counters in the ratio 3:7. What is the probability of red?

    • 7/10
    • 3/4
    • 3/7
    • 3/10

  20. (H) What is the theoretical probability of getting two heads when two fair coins are tossed?

    • 1/3
    • 1/4
    • 1/8
    • 1/2

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