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Probabilities that sum to 1: AQA GCSE Maths questions

Every AQA GCSE Maths exam question on P4 Probabilities that sum to 1, 2017–2025, with its mark scheme and examiner’s report.

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1,304 questions

  1. Q7

    June 2025 · Paper 2H

    3 marksP4 Probabilities that sum to 1
    The whole paper ↗
    June 2025 Paper 2H, question 7: The five possible outcomes of an event are A, B, C, D and E. The table shows some of the probabilities. Outcome A B C D E Probability 0.18 0.2 P(C) = P(B) + 0.1

  2. Q4

    June 2024 · Paper 2H

    4 marksP4 Probabilities that sum to 1
    The whole paper ↗
    June 2024 Paper 2H, question 4: (a) A fair spinner has six equal sections, each with the number 5, 6, 7 or 8 Each number appears at least once. P(even number) = P Work out P You may use the bl

  3. Q13

    November 2022 · Paper 3H

    3 marksP8 Combined events and tree diagramsP4 Probabilities that sum to 1
    The whole paper ↗
    November 2022 Paper 3H, question 13: A fair, ordinary dice is rolled and a counter is taken at random from a bag. The tree diagram shows the probabilities. 13 (a) How do the probabilities show that

  4. Q26

    June 2022 · Paper 1H

    4 marksP8 Combined events and tree diagramsP4 Probabilities that sum to 1
    The whole paper ↗
    June 2022 Paper 1H, question 26: Zoe and Amy are playing a board game. • They each have one disc and take turns to roll a fair, ordinary dice. • The player moves their disc clockwise the number

  5. Q15

    November 2021 · Paper 3H

    3 marksP4 Probabilities that sum to 1
    The whole paper ↗
    November 2021 Paper 3H, question 15: A biased spinner can land on A, B or C. The table shows the probabilities, in terms of k, of A, B and C. A B C Probability 0.5k 7k – 0.15 2.5k Work out the prob

  6. Q11

    November 2020 · Paper 3H

    3 marksP4 Probabilities that sum to 1P3 Relative frequency
    The whole paper ↗
    November 2020 Paper 3H, question 11: A spinner can land on red, blue or green. After 350 spins relative frequency of red = 0.18 relative frequency of blue = 0.62 Work out the number of times the sp

  7. Q17

    November 2019 · Paper 2H

    4 marksP4 Probabilities that sum to 1
    The whole paper ↗
    November 2019 Paper 2H, question 17: A packet contains 80 sweets. The flavour of each sweet is lemon, orange or apple. A sweet is taken at random. 17 (a) P(lemon or orange) ⩽ 0.85 Work out the mini

  8. Q8

    November 2019 · Paper 3H

    5 marksN12 Fractions and percentages as operatorsP4 Probabilities that sum to 1
    The whole paper ↗
    November 2019 Paper 3H, question 8: In a choir there are 35 men and 48 women. The probability that a man chosen at random wears glasses is 5 2 The probability that a woman chosen at random wears g

  9. Q18

    June 2019 · Paper 2H

    3 marksP4 Probabilities that sum to 1R4 Ratio notation
    The whole paper ↗
    June 2019 Paper 2H, question 18: In a bag there are blue discs, green discs and white discs. There are four times as many blue discs as green discs. number of blue discs : number of white discs

  10. Q11

    November 2017 · Paper 1H

    4 marksS2 Charts and tablesP4 Probabilities that sum to 1
    The whole paper ↗
    November 2017 Paper 1H, question 11: The four candidates in an election were A, B, C and D. The pie chart shows the proportion of votes for each candidate. Work out the probability that a person wh

  11. Q5

    June 2017 · Paper 2H

    3 marksP4 Probabilities that sum to 1N5 Systematic listing and the product rule
    The whole paper ↗
    June 2017 Paper 2H, question 5: A code has 4 digits. Each digit is a number from 0 to 9 Digits may be repeated. The code starts 5 4 1 5 4 1 5 (a) Amy knows the last digit is odd but not 7 She

  12. Q9

    June 2017 · Paper 2H

    4 marksP4 Probabilities that sum to 1
    The whole paper ↗
    June 2017 Paper 2H, question 9: The table shows information about some CDs. Type Rock Pop Jazz Number of CDs 2 x 2x + 5 A CD is chosen at random. The probability it is rock is 20 1 Work out th

  13. Q9

    June 2017 · Paper 3H

    5 marksN12 Fractions and percentages as operatorsP4 Probabilities that sum to 1
    The whole paper ↗
    June 2017 Paper 3H, question 9: There are 720 boys and 700 girls in a school. The probability that a boy chosen at random studies French is 3 2 The probability that a girl chosen at random stu

  14. Q14

    Specimen · Paper 1H

    5 marksP4 Probabilities that sum to 1
    The whole paper ↗
    Specimen Paper 1H, question 14: A prime number between 300 and 450 is chosen at random. The table shows the probability that the number lies in different ranges. Prime number, n Probability 30

  15. Q6

    Specimen · Paper 3H

    4 marksP4 Probabilities that sum to 1A17 Linear equations
    The whole paper ↗
    Specimen Paper 3H, question 6: A bag contains counters that are red, blue, green or yellow. red blue green yellow Number of counters 9 3x x – 5 2x A counter is chosen at random. The probabili
All 15 questions on Probabilities that sum to 1, as a list
  1. June 2025, Paper 2H, Q7 (3 marks): The five possible outcomes of an event are A, B, C, D and E. The table shows some of the probabilities. Outcome A B C D E Probability 0.18 0.2 P(C) = P(B) + 0.1
  2. June 2024, Paper 2H, Q4 (4 marks): (a) A fair spinner has six equal sections, each with the number 5, 6, 7 or 8 Each number appears at least once. P(even number) = P Work out P You may use the bl
  3. November 2022, Paper 3H, Q13 (3 marks): A fair, ordinary dice is rolled and a counter is taken at random from a bag. The tree diagram shows the probabilities. 13 (a) How do the probabilities show that
  4. June 2022, Paper 1H, Q26 (4 marks): Zoe and Amy are playing a board game. • They each have one disc and take turns to roll a fair, ordinary dice. • The player moves their disc clockwise the number
  5. November 2021, Paper 3H, Q15 (3 marks): A biased spinner can land on A, B or C. The table shows the probabilities, in terms of k, of A, B and C. A B C Probability 0.5k 7k – 0.15 2.5k Work out the prob
  6. November 2020, Paper 3H, Q11 (3 marks): A spinner can land on red, blue or green. After 350 spins relative frequency of red = 0.18 relative frequency of blue = 0.62 Work out the number of times the sp
  7. November 2019, Paper 2H, Q17 (4 marks): A packet contains 80 sweets. The flavour of each sweet is lemon, orange or apple. A sweet is taken at random. 17 (a) P(lemon or orange) ⩽ 0.85 Work out the mini
  8. November 2019, Paper 3H, Q8 (5 marks): In a choir there are 35 men and 48 women. The probability that a man chosen at random wears glasses is 5 2 The probability that a woman chosen at random wears g
  9. June 2019, Paper 2H, Q18 (3 marks): In a bag there are blue discs, green discs and white discs. There are four times as many blue discs as green discs. number of blue discs : number of white discs
  10. November 2017, Paper 1H, Q11 (4 marks): The four candidates in an election were A, B, C and D. The pie chart shows the proportion of votes for each candidate. Work out the probability that a person wh
  11. June 2017, Paper 2H, Q5 (3 marks): A code has 4 digits. Each digit is a number from 0 to 9 Digits may be repeated. The code starts 5 4 1 5 4 1 5 (a) Amy knows the last digit is odd but not 7 She
  12. June 2017, Paper 2H, Q9 (4 marks): The table shows information about some CDs. Type Rock Pop Jazz Number of CDs 2 x 2x + 5 A CD is chosen at random. The probability it is rock is 20 1 Work out th
  13. June 2017, Paper 3H, Q9 (5 marks): There are 720 boys and 700 girls in a school. The probability that a boy chosen at random studies French is 3 2 The probability that a girl chosen at random stu
  14. Specimen, Paper 1H, Q14 (5 marks): A prime number between 300 and 450 is chosen at random. The table shows the probability that the number lies in different ranges. Prime number, n Probability 30
  15. Specimen, Paper 3H, Q6 (4 marks): A bag contains counters that are red, blue, green or yellow. red blue green yellow Number of counters 9 3x x – 5 2x A counter is chosen at random. The probabili

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