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GCSE Maths · Edexcel 1MA1 · Grade Ladder · Probability and statistics

Grade Ladder: Probability and Statistics

18 questions climbing from grade 1 to grade 9 across the probability and statistics content of the Edexcel GCSE, two at each grade. Each question shows its grade, its specification code and whether it is non-calculator.

How to use this ladderFoundation students: work through Grades 1–5. Higher students: start at Grade 4 and push on to 9. Questions marked Non-calculator should be done without a calculator, as in Paper 1.
Grades 1–3 · Foundation
  1. (1 mark)
    Grade 1P3Non-calculator
    A fair coin is flipped. What is the probability of a head?
  2. (1 mark)
    Grade 1S4Non-calculator
    Find the mode of 3, 5, 5, 7, 9.
  3. (2 marks)
    Grade 2P3Non-calculator
    A fair dice is rolled. Find (a) P(even) (b) P(greater than 4).
  4. (1 mark)
    Grade 2S4Non-calculator
    Find the mean of 4, 7, 9, 12.
  5. (2 marks)
    Grade 3S4Non-calculator
    Find the median and the range of 12, 5, 9, 15, 7, 10.
  6. (1 mark)
    Grade 3P4Non-calculator
    P(red) = 0.35. Find P(not red).
Grades 4–5 · Foundation and Higher
  1. (2 marks)
    Grade 4P3Non-calculator
    The probability of winning a game is 0.15. Anna plays 300 times. How many times should she expect to win?
  2. (2 marks)
    Grade 4S2Non-calculator
    In a survey of 60 people, 15 chose tea. What angle should tea have in a pie chart?
  3. (2 marks)
    Grade 5P8Non-calculator
    Two fair coins are flipped. Find the probability of two heads.
  4. (3 marks)
    Grade 5S4
    Estimate the mean.
    Time t (s)0 < t ≤ 1010 < t ≤ 2020 < t ≤ 30
    Frequency4106
Grades 6–7 · Higher
  1. (3 marks)
    Grade 6P8Non-calculator
    A bag has 3 red and 5 blue counters. A counter is taken, replaced, and a second is taken. Find P(both red).
  2. (2 marks)
    Grade 6S6Non-calculator
    A scatter graph shows that as temperature rises, ice-cream sales rise. Describe the correlation, and explain why it doesn’t prove that heat causes sales.
  3. (3 marks)
    Grade 7P8Non-calculator
    A bag has 3 red and 5 blue counters. Two are taken without replacement. Find P(both the same colour).
  4. (2 marks)
    Grade 7S3Non-calculator
    On a histogram, the class 10 < t ≤ 20 has frequency density 2.4. Find its frequency.
Grades 8–9 · Higher
  1. (3 marks)
    Grade 8P9Non-calculator
    In a Venn diagram, A only = 12, A ∩ B = 8, B only = 10 and neither = 10. Find P(A | B).
  2. (2 marks)
    Grade 8S3Non-calculator
    On a histogram, the class 15 < t ≤ 30 has frequency density 1.6. Find its frequency.
  3. (3 marks)
    Grade 9P8Non-calculator
    A fair dice is rolled three times. Find the probability of getting at least one six.
  4. (4 marks)
    Grade 9P8Non-calculator
    A bag has n counters, 4 of which are red. Two are taken without replacement. P(both red) = 314. Find n.
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Worked solutions

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GCSE Maths · Edexcel 1MA1 · Grade Ladder · Probability and statistics

Grade Ladder: Probability and Statistics — Worked Solutions

Full worked solutions to all 18 questions (39 marks).

Grades 1–3 · Foundation
  1. (1 mark)
    Grade 1P3Non-calculator
    A fair coin is flipped. What is the probability of a head?
    Solution
    1. 2 equally likely outcomes.
    12
  2. (1 mark)
    Grade 1S4Non-calculator
    Find the mode of 3, 5, 5, 7, 9.
    Solution
    1. The most common value.
    5
  3. (2 marks)
    Grade 2P3Non-calculator
    A fair dice is rolled. Find (a) P(even) (b) P(greater than 4).
    Solution
    1. (a) 2, 4, 6 → 3 out of 6.
    2. (b) 5, 6 → 2 out of 6.
    (a) ½ (b) ⅓
  4. (1 mark)
    Grade 2S4Non-calculator
    Find the mean of 4, 7, 9, 12.
    Solution
    1. 32 ÷ 4.
    8
  5. (2 marks)
    Grade 3S4Non-calculator
    Find the median and the range of 12, 5, 9, 15, 7, 10.
    Solution
    1. Order: 5, 7, 9, 10, 12, 15. Median = (9 + 10) ÷ 2.
    2. Range = 15 − 5.
    Median 9.5, range 10
  6. (1 mark)
    Grade 3P4Non-calculator
    P(red) = 0.35. Find P(not red).
    Solution
    1. 1 − 0.35.
    0.65
Grades 4–5 · Foundation and Higher
  1. (2 marks)
    Grade 4P3Non-calculator
    The probability of winning a game is 0.15. Anna plays 300 times. How many times should she expect to win?
    Solution
    1. 0.15 × 300.
    45
  2. (2 marks)
    Grade 4S2Non-calculator
    In a survey of 60 people, 15 chose tea. What angle should tea have in a pie chart?
    Solution
    1. 1560 × 360°.
    90°
  3. (2 marks)
    Grade 5P8Non-calculator
    Two fair coins are flipped. Find the probability of two heads.
    Solution
    1. ½ × ½.
    14
  4. (3 marks)
    Grade 5S4
    Estimate the mean.
    Time t (s)0 < t ≤ 1010 < t ≤ 2020 < t ≤ 30
    Frequency4106
    Solution
    1. Midpoints 5, 15, 25.
    2. Σfx = 20 + 150 + 150 = 320; Σf = 20.
    3. 320 ÷ 20.
    16 s
Grades 6–7 · Higher
  1. (3 marks)
    Grade 6P8Non-calculator
    A bag has 3 red and 5 blue counters. A counter is taken, replaced, and a second is taken. Find P(both red).
    Solution
    1. 38 × 38.
    964
  2. (2 marks)
    Grade 6S6Non-calculator
    A scatter graph shows that as temperature rises, ice-cream sales rise. Describe the correlation, and explain why it doesn’t prove that heat causes sales.
    Solution
    1. Positive correlation.
    2. Correlation shows a relationship, not cause: another factor (such as summer holidays) could affect both.
    Positive correlation; correlation ≠ causation
  3. (3 marks)
    Grade 7P8Non-calculator
    A bag has 3 red and 5 blue counters. Two are taken without replacement. Find P(both the same colour).
    Solution
    1. P(RR) = 38 × 27 = 656.
    2. P(BB) = 58 × 47 = 2056.
    3. Add: 2656.
    1328
  4. (2 marks)
    Grade 7S3Non-calculator
    On a histogram, the class 10 < t ≤ 20 has frequency density 2.4. Find its frequency.
    Solution
    1. Frequency = FD × class width = 2.4 × 10.
    24
Grades 8–9 · Higher
  1. (3 marks)
    Grade 8P9Non-calculator
    In a Venn diagram, A only = 12, A ∩ B = 8, B only = 10 and neither = 10. Find P(A | B).
    Solution
    1. Given B: total 8 + 10 = 18.
    2. In A as well: 8.
    49
  2. (2 marks)
    Grade 8S3Non-calculator
    On a histogram, the class 15 < t ≤ 30 has frequency density 1.6. Find its frequency.
    Solution
    1. Width 15: 1.6 × 15.
    24
  3. (3 marks)
    Grade 9P8Non-calculator
    A fair dice is rolled three times. Find the probability of getting at least one six.
    Solution
    1. P(no six) = (56)³ = 125216.
    2. 1 − 125216.
    91216
  4. (4 marks)
    Grade 9P8Non-calculator
    A bag has n counters, 4 of which are red. Two are taken without replacement. P(both red) = 314. Find n.
    Solution
    1. 4n × 3n − 1 = 314 → 12n(n − 1) = 314 → n(n − 1) = 56.
    2. n² − n − 56 = 0 → (n − 8)(n + 7) = 0, and n > 0.
    n = 8
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