Lemmara logoLemmaraWorked solution

4MA1/2H Jun 2020, Question 20: Tree Diagrams for Dependent Events

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

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

A bag holds X counters, red and blue only, with 4 more blue than red. Taking 2 counters at random gives probability 3/8 of both being blue. Find X using clear algebra.

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

Solution · 5 marks

  1. 1Let the number of red counters be r. Then blue counters = r + 4. Total counters X = r + (r + 4) = 2r + 4.
  2. 2Probability first counter is blue = (r + 4) / (2r + 4)
  3. 3Probability second counter is blue = (r + 3) / (2r + 3)
  4. 4Probability both counters are blue = [(r + 4)/(2r + 4)] × [(r + 3)/(2r + 3)] = 3/8
  5. 5So: (r + 4)(r + 3) / [(2r + 4)(2r + 3)] = 3/8
  6. 6Multiply both sides by 8(2r + 4)(2r + 3): 8(r + 4)(r + 3) = 3(2r + 4)(2r + 3)
  7. 7Expand left: 8(r² + 7r + 12) = 8r² + 56r + 96
  8. 8Expand right: 3(4r² + 6r + 8r + 12) = 3(4r² + 14r + 12) = 12r² + 42r + 36
  9. 9Bring all to one side: 8r² + 56r + 96 − (12r² + 42r + 36) = 0
  10. 10−4r² + 14r + 60 = 0
  11. 11Multiply by −1: 4r² − 14r − 60 = 0
  12. 12Divide by 2: 2r² − 7r − 30 = 0
  13. 13Factorise: (2r + 5)(r − 6) = 0
  14. 14So r = 6 (since r cannot be negative)
  15. 15Then blue counters = 6 + 4 = 10
  16. 16Total counters X = 6 + 10 = 16

Answer16

Stuck on a step? Read the free lesson: Tree Diagrams for Dependent Events

Practise more tree diagrams for dependent events 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 tree diagrams for dependent events

Also searched as: 4MA1 2H June 2020 · 4MA1/2H · 4ma1 jun20 2h · question 20.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.