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0580/22 May/Jun 2022, Question 16: Conditional Probability

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 4 marks

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The question, in short

Venn diagram with 40 students studying physics, mathematics and geography; use set notation for a shaded region, evaluate a set expression, and find a conditional probability.

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

Part (a) · 1 mark

Describe the shaded region using set notation.

  1. 1Shaded regions (11, 5, 6) are in M or G but not in P
  2. 2(M ∪ G) ∩ P′

Answer(M ∪ G) ∩ P′

Part (b) · 1 mark

Find n((P ∩ G) ∪ M′).

  1. 1P ∩ G = 3 + 9 = 12, M′ = 4 + 3 + 6 = 13
  2. 23 is in both, so n((P ∩ G) ∪ M′) = 12 + 13 − 3
  3. 3= 22

Answer22

Part (c) · 2 marks

Given the chosen student studies geography, find the probability they study physics or mathematics but not both.

  1. 1n(G) = 3 + 9 + 5 + 6 = 23
  2. 2Physics or maths but not both: 3 + 5 = 8
  3. 3Probability = 8/23

Answer8/23

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Also searched as: 0580/22/M/J/22 · 0580_s22_qp_22 · 0580 s22 22 · question 16.
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