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0580/21 May/Jun 2025, Question 17: Tree Diagrams for Dependent Events

Cambridge IGCSE Mathematics 0580 · Paper 21 (Extended) · Non-calculator · 7 marks

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The question, in short

Bag with 6 red, 3 green, 1 blue marble; two picked with replacement. Second bag has 4 red, 2 yellow counters; two picked without replacement. Find probabilities and complete tree diagram.

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

Part (a) · 2 marks

Find the probability that both marbles picked with replacement are green.

  1. 1P(green) = 3/10 each time
  2. 2P(both green) = 3/10 × 3/10 = 9/100

Answer9/100

Part (bi) · 2 marks

Complete the tree diagram for two counters drawn without replacement, filling in the missing fractions.

  1. 1After red: 3 red, 2 yellow left of 5, so Yellow = 2/5
  2. 2After yellow: 4 red, 1 yellow left of 5, so Red = 4/5, Yellow = 1/5

AnswerRed then Yellow: 2/5 Yellow then Red: 4/5 Yellow then Yellow: 1/5

Part (bii) · 3 marks

Find the probability that exactly one of the two counters is yellow.

  1. 1P(RY) = 4/6 × 2/5 = 8/30
  2. 2P(YR) = 2/6 × 4/5 = 8/30
  3. 3P(one yellow) = 8/30 + 8/30 = 16/30

Answer16/30

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Also searched as: 0580/21/M/J/25 · 0580_s25_qp_21 · 0580 s25 21 · question 17.
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