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4MA1/1HR Jun 2020, Question 23: Tree Diagrams for Dependent Events

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 4 marks

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The question, in short

A bag holds 3 blue, 4 white and x orange beads; two are drawn at random and the chance both match in colour is 3/8. Determine how many beads are in the bag, showing algebra.

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

Solution · 4 marks

  1. 1Total beads = 3 + 4 + x = 7 + x
  2. 2P(two blue) = (3/(7+x)) × (2/(6+x))
  3. 3P(two white) = (4/(7+x)) × (3/(6+x))
  4. 4P(two orange) = (x/(7+x)) × ((x−1)/(6+x))
  5. 5Sum of probabilities = 3/8
  6. 6(3×2 + 4×3 + x(x−1)) / ((7+x)(6+x)) = 3/8
  7. 7(6 + 12 + x² − x) / (x² + 13x + 42) = 3/8
  8. 8(x² − x + 18) / (x² + 13x + 42) = 3/8
  9. 98(x² − x + 18) = 3(x² + 13x + 42)
  10. 108x² − 8x + 144 = 3x² + 39x + 126
  11. 115x² − 47x + 18 = 0
  12. 12(5x − 2)(x − 9) = 0
  13. 13x = 9 (since x must be a positive integer)
  14. 14Total beads = 7 + 9 = 16

Answer16

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