4MA1/2H Jun 2021, 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
Box has N pens, black and red only, with 3 more black than red. Taking 2 pens at random, probability black then red is 9/35. Find possible values of N, showing algebraic working.
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Solution · 5 marks
- 1Red pens = r, black pens = r + 3, so N = 2r + 3
- 2(r + 3)/(2r + 3) × r/(2r + 2) = 9/35, so 35r(r + 3) = 9(2r + 3)(2r + 2)
- 335r² + 105r = 36r² + 90r + 54, so r² − 15r + 54 = 0
- 4(r − 6)(r − 9) = 0, so r = 6 or r = 9
- 5N = 2r + 3 gives 21, 15
Answer21, 15
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