4MA1/1HR Jun 2025, Question 19: Tree Diagrams for Dependent Events
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 3 marks
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The question, in short
From counters numbered 1, 1, 2, 3, 3, 3, 5, 6, 6, two are drawn without replacement; find the probability that the two numbers add to less than 5.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 3 marks
- 1Pairs with sum < 5: (1,1), (1,2), (2,1), (1,3), (3,1)
- 2P(1,1) = 2/9 × 1/8 = 2/72
- 3P(1,2) + P(2,1) = 2/9 × 1/8 + 1/9 × 2/8 = 4/72
- 4P(1,3) + P(3,1) = 2/9 × 3/8 + 3/9 × 2/8 = 12/72
- 5Total = 18/72 = 1/4
Answer1/4
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