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4024/22 May/Jun 2025, Question 13: Tree Diagrams for Dependent Events

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 3 marks

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The question, in short

A bag holds 9 red and 3 green counters; Lee draws two without replacement. Fill in the tree diagram and find the probability both counters are red.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 2 marks

Complete the tree diagram by filling in the missing fractions on the first and second counter branches.

  1. 1First counter: Green = 3/12 (since 9/12 + 3/12 = 1)
  2. 2After Red: 11 left, 8 red and 3 green, so Green = 3/11
  3. 3After Green: 11 left, 9 red and 2 green, so Red = 9/11, Green = 2/11

AnswerFirst counter: Green 3/12 Second counter: after Red, Green 3/11; after Green, Red 9/11 and Green 2/11

Part (b) · 1 mark

Calculate the probability that both counters taken are red.

  1. 1P(red, red) = 9/12 × 8/11 = 72/132
  2. 2= 6/11

Answer6/11

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Also searched as: 4024/22/M/J/25 · 4024_s25_qp_22 · 4024 s25 22 · question 13.
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