4MA1/2HR Jan 2021, Question 21: Tree Diagrams for Dependent Events
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 6 marks
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The question, in short
Bag has n beads, 6 red and rest blue; two drawn at random. Given probability both same colour is 9/17, use algebra to find n, showing all working.
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Solution · 6 marks
- 1There are n − 6 blue beads
- 2P(same) = 6/n × 5/(n − 1) + (n − 6)/n × (n − 7)/(n − 1) = 9/17
- 317(30 + (n − 6)(n − 7)) = 9n(n − 1), which simplifies to 2n² − 53n + 306 = 0
- 4(2n − 17)(n − 18) = 0, so n = 8.5 or n = 18
- 5n must be a whole number, so n = 18
Answer18
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