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4MA1/2FR Jun 2024, Question 11: Combined Events with Two-Way Tables

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2FR (Foundation) · Calculator · 5 marks

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The question, in short

Café question: list pairs of cake types, complete a two-way table of ice cream sales, and find a probability from 100 students' preferences.

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

Part (a) · 2 marks

List every possible combination of 2 different cake types chosen from C, F, L and M.

  1. 1List all pairs from C, F, L, M
  2. 2C with F, L, M → CF, CL, CM
  3. 3F with L, M → FL, FM
  4. 4L with M → LM
  5. 5CF, CL, CM, FL, FM, LM

AnswerCF, CL, CM, FL, FM, LM

Part (b) · 2 marks

Fill in the missing values in the two-way table for Saturday, Sunday and the totals.

  1. 1The Sunday total is 49, and Sunday has 20 mint and 13 vanilla
  2. 2Sunday chocolate = 49 − 20 − 13 = 16
  3. 3The chocolate total is 48, so Saturday chocolate = 48 − 16 = 32
  4. 4Saturday total = 32 + 11 + 28 = 71
  5. 5Overall total = 71 + 49 = 120
  6. 6Check: 48 + 31 + 41 = 120

AnswerChocolate: Saturday 32, Sunday 16; Mint: Saturday 11, Sunday 20; Vanilla: Saturday 28, Sunday 13; Total Saturday 71, Sunday 49, Total Chocolate 48, Mint 31, Vanilla 41, Overall total 120

Part (c) · 1 mark

With 33 of 100 students preferring cake, find the probability a randomly chosen student does not prefer cake.

  1. 1100 students, 33 prefer cake
  2. 2100 − 33 = 67 do not prefer cake
  3. 3Probability = 67/100

Answer67/100

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