4MA1/2HR Jun 2019, Question 24: Tree Diagrams for Dependent Events
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 5 marks
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The question, in short
A box has 4 red marbles and the rest yellow. Two marbles are taken without replacement; the chance both are yellow is 0.7. Find the original total number of marbles, showing working.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 5 marks
- 1Let x marbles be in the box, so x − 4 are yellow
- 2(x − 4)/x × (x − 5)/(x − 1) = 0.7
- 3(x − 4)(x − 5) = 0.7x(x − 1), so 3x² − 83x + 200 = 0
- 4(3x − 8)(x − 25) = 0, so x = 8/3 or x = 25
- 5x must be a whole number, so x = 25
Answer25
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