Lemmara logoLemmaraWorked solution

4MA1/2F Jun 2019, Question 7: Combined Events with Two-Way Tables

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2F (Foundation) · Calculator · 6 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Complete a multiplication table of spinner and dice scores, find the probability a score exceeds 10, and judge whether the game is unfair by comparing prize 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 for spinner results 1, 2, 3 multiplied by dice results 1 to 6.

  1. 1Multiply spinner number by dice number
  2. 2Missing row 1: 1 × 5 = 5, 1 × 6 = 6
  3. 3Missing row 2: 2 × 1 = 2, 2 × 3 = 6, 2 × 6 = 12
  4. 4Missing row 3: 3 × 3 = 9, 3 × 5 = 15

AnswerRow 1: 1, 2, 3, 4, 5, 6; Row 2: 2, 4, 6, 8, 10, 12; Row 3: 3, 6, 9, 12, 15, 18

Part (b) · 2 marks

Find the probability that Steven's score, spinner times dice, is greater than 10.

  1. 1There are 3 × 6 = 18 equally likely scores
  2. 2Scores greater than 10: 12, 12, 15, 18 (4 scores)
  3. 3P(score > 10) = 4/18

Answer4/18

Part (c) · 2 marks

Compare the probability of scoring 5 or less with the probability of a multiple of 6, and decide if Carmen's claim is correct.

  1. 1Scores 5 or less: 1, 2, 3, 4, 5, 2, 4, 3 (8 scores)
  2. 2Multiples of 6: 6, 6, 12, 6, 12, 18 (6 scores)
  3. 3P(Adam) = 8/18, P(Carmen) = 6/18
  4. 48/18 > 6/18, so Adam is more likely to win: unfair

AnswerYes, the game is unfair: P(Adam) = 8/18 but P(Carmen) = 6/18

Stuck on a step? Read the free lesson: Combined Events with Two-Way Tables

Practise more combined events with two-way tables questions

Real 4MA1 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on combined events with two-way tables

Also searched as: 4MA1 2F June 2019 · 4MA1/2F · 4ma1 jun19 2f · question 7.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.