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4024/22 Oct/Nov 2025, Question 19: Tree Diagrams for Dependent Events

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 5 marks

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The question, in short

Use a Venn diagram for 22 students studying Economics (E) or History (H) to read set values and find a three-student selection probability.

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

Part (a) · 1 mark

State how many students study both Economics and History from the diagram.

  1. 1Both E and H: the overlap, 5

Answer5

Part (b) · 1 mark

Find n(E ∩ H′), the number studying Economics but not History.

  1. 1E ∩ H′ = in E but not in H = 7

Answer7

Part (c) · 3 marks

For three students chosen at random, find the probability all study History.

  1. 1n(H) = 5 + 4 = 9 out of 22
  2. 2P(all three study History) = 9/22 × 8/21 × 7/20
  3. 3= 504/9240 = 3/55

Answer3/55

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Also searched as: 4024/22/O/N/25 · 4024_w25_qp_22 · 4024 w25 22 · question 19.
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