4MA1/2H Jun 2019, Question 23: Tree Diagrams for Dependent Events
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 5 marks
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The question, in short
Bag holds only red and green sweets, 3 red originally. Taking 2 at random gives probability 12/35 of exactly 1 red. Find the original number of green sweets, showing working.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 5 marks
- 1Let n = total sweets: 3 red and n − 3 green
- 2P(exactly 1 red) = 2 × 3/n × (n − 3)/(n − 1) = 12/35
- 335 × 6(n − 3) = 12n(n − 1), so 12n² − 222n + 630 = 0
- 42n² − 37n + 105 = 0, so (2n − 7)(n − 15) = 0, n = 15
- 5Green sweets = 15 − 3 = 12
Answer12
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