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0580/42 Feb/Mar 2023, Question 7: Tree Diagrams for Dependent Events

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 9 marks

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The question, in short

Use set sizes for a class of 24, with Physics 17, Chemistry 14 and 9 in both, to complete a Venn diagram and answer counting and probability questions.

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

Part (a) · 2 marks

Fill the Venn diagram regions for Physics only, Chemistry only, and students outside both subjects using the given set sizes.

  1. 1P only = 17 − 9 = 8
  2. 2C only = 14 − 9 = 5
  3. 3Outside = 24 − (8 + 9 + 5) = 2
  4. 4P only 8, P ∩ C 9, C only 5, outside 2

AnswerP only: 8 P ∩ C: 9 C only: 5 Outside P and C: 2

Part (bi) · 1 mark

Find the number of students who study Physics but not Chemistry.

  1. 1P ∩ C′ = in P but not C
  2. 2n(P ∩ C′) = 8

Answer8

Part (bii) · 1 mark

Find the number of students in Physics or not in Chemistry.

  1. 1P ∪ C′ = everyone except those in C only
  2. 2n(P ∪ C′) = 24 − 5 = 19

Answer19

Part (c) · 3 marks

For two students chosen at random, find the probability of selecting one who studies both subjects and one who studies Chemistry only.

  1. 1P(both, then C only) = 9/24 × 5/23
  2. 2Either order: 2 × 9/24 × 5/23
  3. 3= 90/552 = 15/92

Answer15/92

Part (d) · 2 marks

Given two Physics students are chosen at random, find the probability that both also study Chemistry.

  1. 19 of the 17 Physics students study Chemistry
  2. 2P = 9/17 × 8/16
  3. 3= 72/272 = 9/34

Answer9/34

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Also searched as: 0580/42/F/M/23 · 0580_m23_qp_42 · 0580 m23 42 · question 7.
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