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0580/41 May/Jun 2021, Question 6: Conditional Probability

Cambridge IGCSE Mathematics 0580 · Paper 41 (Extended) · Calculator · 12 marks

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The question, in short

Venn diagram questions: shade a set region, complete a two-set diagram from 50 students' phone and computer data, then use a three-set diagram of 30 students to find counts, set notation, and probabilities.

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

Part (a) · 1 mark

Shade the region representing P′ ∪ Q on the given two-circle Venn diagram.

  1. 1P′ is everything outside P; union with Q adds the overlap
  2. 2Shade Q and the region outside both circles (leave P only unshaded)

AnswerShaded: Q and the region outside P (everything except P only)

Part (b) · 2 marks

Place the four region values in the Venn diagram for 50 students, using 34 with M, 39 with C, and 5 with neither.

  1. 1Outside both = 5, so n(M ∪ C) = 50 − 5 = 45
  2. 2n(M ∩ C) = 34 + 39 − 45 = 28
  3. 3M only = 34 − 28 = 6, C only = 39 − 28 = 11

AnswerM only: 6 M ∩ C: 28 C only: 11 Outside M and C: 5

Part (ci) · 1 mark

State how many students have brothers, reading from the three-set diagram.

  1. 1n(B) = 2 + 2 + 3 + 1 = 8

Answer8

Part (cii) · 1 mark

State how many students have cousins but not sisters, using the diagram.

  1. 1C but not S = 8 + 3 = 11

Answer11

Part (ciii) · 1 mark

Find n(B ∪ S ∪ C)′, the number outside all three circles.

  1. 1Outside all three circles: n(B ∪ S ∪ C)′ = 2

Answer2

Part (civ) · 1 mark

Write set notation for students with both cousins and sisters but no brothers.

  1. 1Cousins and sisters, not brothers: C ∩ S ∩ B′

AnswerC ∩ S ∩ B′

Part (cv) · 1 mark

Find the probability a randomly chosen student from the 30 has cousins.

  1. 1n(C) = 8 + 3 + 7 + 1 = 19
  2. 2P(cousins) = 19/30

Answer19/30

Part (cvi) · 3 marks

For two students chosen at random from those with cousins, calculate the probability both have brothers.

  1. 1Of the 19 with cousins, 3 + 1 = 4 have brothers
  2. 2P = 4/19 × 3/18 = 12/342 = 2/57

Answer2/57

Part (cvii) · 1 mark

Explain why having sisters and having cousins but not brothers are equally likely events.

  1. 1n(A) = 5 + 2 + 7 + 1 = 15, n(B) = 8 + 7 = 15
  2. 2Equal numbers, so both probabilities are 15/30

AnswerEqual numbers, 15 each, or equal probability 15/30

Stuck on a step? Read the free lesson: Conditional Probability

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Also searched as: 0580/41/M/J/21 · 0580_s21_qp_41 · 0580 s21 41 · question 6.
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