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0580/22 May/Jun 2024, Question 23: Conditional Probability

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 3 marks

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The question, in short

Use the Venn diagram counts for students studying English, French and Spanish to answer a set-notation question and a probability question about Spanish students.

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

Part (a) · 1 mark

Find n((E ∪ F)′ ∪ S) using the numbers in the Venn diagram.

  1. 1(E ∪ F)′ = S only 4 + none 5 = 9 students
  2. 2S = 2 + 1 + 3 + 4 = 10 students
  3. 3(E ∪ F)′ ∪ S = 4 + 5 + 2 + 1 + 3 = 15

Answer15

Part (b) · 2 marks

Given a student studies Spanish, find the probability they study exactly two languages.

  1. 1Students who study Spanish: 2 + 1 + 3 + 4 = 10
  2. 2Exactly two languages: E ∩ S only 2 + F ∩ S only 3 = 5
  3. 3Probability = 5/10 = 1/2

Answer1/2

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Also searched as: 0580/22/M/J/24 · 0580_s24_qp_22 · 0580 s24 22 · question 23.
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