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4024/23 May/Jun 2026, Question 10: Tree Diagrams for Independent Events

Cambridge O Level Mathematics 4024 · Paper 23 (Calculator) · Calculator · 3 marks

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The question, in short

A bag holds red and yellow counters; red has probability 0.3. A counter is picked, replaced, then a second is picked. Complete a tree diagram and find the probability both are yellow.

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

Part (a) · 2 marks

Fill in the missing probabilities on the tree diagram for the first and second picks, given red is 0.3.

  1. 1P(yellow) = 1 − 0.3 = 0.7
  2. 2The counter is replaced, so the second-counter probabilities are the same
  3. 3Red branches 0.3, yellow branches 0.7

Answer0.3 for every red branch and 0.7 for every yellow branch

Part (b) · 1 mark

Calculate the probability that the first and second counters chosen are both yellow.

  1. 1P(yellow, yellow) = 0.7 × 0.7
  2. 2= 0.49

Answer0.49

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