4MA1/1HR Jun 2024, Question 21: Tree Diagrams for Dependent Events
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 5 marks
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The question, in short
Bag has 25 counters: 6 blue, x orange (x > 9), rest pink. Two drawn at random; P(one orange, one pink) = 22/75. Find P(two pink), showing algebra.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 5 marks
- 1Pink counters = 25 − 6 − x = 19 − x
- 2P(orange and pink) = 2 × x/25 × (19 − x)/24 = 22/75, so x(19 − x) = 88
- 3x² − 19x + 88 = 0, so (x − 11)(x − 8) = 0; x > 9 gives x = 11
- 4Pink = 19 − 11 = 8 counters
- 5P(2 pink) = 8/25 × 7/24 = 56/600 = 7/75
Answer7/75
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