4024/12 May/Jun 2022, Question 22: Tree Diagrams for Dependent Events
Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 4 marks
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The question, in short
Nine letter tiles spell ISOSCELES: probability of not picking E with replacement, then of two matching letters picked without replacement.
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Part (a) · 1 mark
One tile, returned afterwards: probability it is not E.
- 1There are 2 E tiles, so 7 tiles are not E
- 2P(not E) = 7/9
Answer7/9
Part (b) · 3 marks
Two tiles without replacement: probability the letters match.
- 1Letters that repeat: S (3 tiles) and E (2 tiles)
- 2P(S, S) = 3/9 × 2/8 = 6/72
- 3P(E, E) = 2/9 × 1/8 = 2/72
- 4P(same letter) = 6/72 + 2/72 = 8/72 = 1/9
Answer1/9 or 8/72
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