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0580/42 May/Jun 2025, Question 22: Tree Diagrams for Dependent Events

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 5 marks

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The question, in short

Using a Venn diagram for 33 students with geography G and history H, calculate probabilities from the given region counts.

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

Part (ai) · 1 mark

Find the chance a randomly chosen student is in neither G nor H.

  1. 1Neither geography nor history: 5 students
  2. 2P = 5/33

Answer5/33

Part (aii) · 1 mark

Find the chance a randomly chosen student is in both G and H.

  1. 1Both: 13 students
  2. 2P = 13/33

Answer13/33

Part (b) · 3 marks

Two history students are chosen; find the chance exactly one also studies geography.

  1. 1History students = 13 + 7 = 20 (13 study geography, 7 do not)
  2. 2P(G then not G) = 13/20 × 7/19 = 91/380
  3. 3P(not G then G) = 7/20 × 13/19 = 91/380
  4. 4P = 2 × 91/380 = 91/190

Answer91/190

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Also searched as: 0580/42/M/J/25 · 0580_s25_qp_42 · 0580 s25 42 · question 22.
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