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4MA1/2F Jun 2022, 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

Two fair spinners, A with 1 to 3 and B with 2, 4, 6, 8, 10, are spun once and scores added; complete a totals table and 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 cells of the two-way table showing every possible sum of a spinner A result and a spinner B result.

  1. 1Each entry is the spinner A number added to the spinner B number
  2. 2Row B = 2: 1 + 2 = 3, 2 + 2 = 4, 3 + 2 = 5
  3. 3Row B = 4: 1 + 4 = 5, 2 + 4 = 6, 3 + 4 = 7
  4. 4Row B = 6: 1 + 6 = 7, 2 + 6 = 8, 3 + 6 = 9
  5. 5Row B = 8: 1 + 8 = 9, 2 + 8 = 10, 3 + 8 = 11
  6. 6Row B = 10: 1 + 10 = 11, 2 + 10 = 12, 3 + 10 = 13

AnswerRow B = 2: 3, 4, 5; row B = 4: 5, 6, 7; row B = 6: 7, 8, 9; row B = 8: 9, 10, 11; row B = 10: 11, 12, 13 (reading across for spinner A = 1, 2, 3)

Part (bi) · 1 mark

Work out the probability that the combined score from the two spinners is an odd number.

  1. 1There are 3 × 5 = 15 equally likely total scores in the table
  2. 2The odd totals are 3, 5, 5, 7, 7, 9, 9, 11, 11 and 13
  3. 3That is 10 odd totals out of 15
  4. 4P(total score is odd) = 10/15

Answer10/15

Part (bii) · 1 mark

Work out the probability that the combined score from the two spinners is below 9.

  1. 1There are 15 equally likely total scores in the table
  2. 2The totals less than 9 are 3, 4, 5, 5, 6, 7, 7 and 8
  3. 3That is 8 totals out of 15
  4. 4P(total score is less than 9) = 8/15

Answer8/15

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