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4MA1/2F Jun 2024, Question 5: Combined Events with Two-Way Tables

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2F (Foundation) · Calculator · 4 marks

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The question, in short

Percy spins two fair spinners, A (1, 1, 2, 3) and B (5, 7, 8, 9, 11), and subtracts A from B. Complete the score table, then find two probabilities.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 2 marks

Fill in the missing score cells in the table by subtracting each spinner A value from each spinner B value.

  1. 1Each score is the spinner B number minus the spinner A number
  2. 2Row 5: 5 − 1 = 4, 5 − 1 = 4, 5 − 2 = 3, 5 − 3 = 2
  3. 3Row 7: 7 − 1 = 6, 7 − 1 = 6, 7 − 2 = 5, 7 − 3 = 4
  4. 4Row 8: 8 − 1 = 7, 8 − 1 = 7, 8 − 2 = 6, 8 − 3 = 5
  5. 5Row 9: 9 − 1 = 8, 9 − 1 = 8, 9 − 2 = 7, 9 − 3 = 6
  6. 6Row 11: 11 − 1 = 10, 11 − 1 = 10, 11 − 2 = 9, 11 − 3 = 8
  7. 7The completed table, row by row, is 4, 4, 3, 2 / 6, 6, 5, 4 / 7, 7, 6, 5 / 8, 8, 7, 6 / 10, 10, 9, 8

AnswerReading across each spinner B row against the spinner A columns 1, 1, 2, 3 — row 5: 4, 4, 3, 2; row 7: 6, 6, 5, 4; row 8: 7, 7, 6, 5; row 9: 8, 8, 7, 6; row 11: 10, 10, 9, 8

Part (bi) · 1 mark

Find the probability that Percy's score is an even number.

  1. 1The table has 4 × 5 = 20 equally likely scores
  2. 2Even scores in row 5: 4, 4, 2 — that is 3
  3. 3Even scores in row 7: 6, 6, 4 — that is 3
  4. 4Even score in row 8: 6 — that is 1
  5. 5Even scores in row 9: 8, 8, 6 — that is 3
  6. 6Even scores in row 11: 10, 10, 8 — that is 3
  7. 7Number of even scores = 3 + 3 + 1 + 3 + 3 = 13
  8. 8P(score is even) = 13/20

Answer13/20

Part (bii) · 1 mark

Find the probability that Percy's score is greater than 7.

  1. 1The scores greater than 7 are 8 and 8 in row 9
  2. 2and 10, 10, 9 and 8 in row 11
  3. 3Number of scores greater than 7 = 2 + 4 = 6 out of 20
  4. 4P(score is greater than 7) = 6/20

Answer6/20

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