0580/22 Feb/Mar 2023, Question 24: Tree Diagrams for Independent Events
Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 2 marks
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The question, in short
Given Jamie's hit probability is 1/3 and the first hit occurs on attempt n with probability 64/2187, find n.
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Solution · 2 marks
- 1Miss n − 1 times then hit: (2/3)ⁿ⁻¹ × 1/3 = 64/2187
- 264/2187 = 2⁶/3⁷ = (2/3)⁶ × 1/3
- 3n − 1 = 6, so n = 7
Answer7
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