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0580/41 May/Jun 2022, Question 8: Tree Diagrams for Independent Events

Cambridge IGCSE Mathematics 0580 · Paper 41 (Extended) · Calculator · 14 marks

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The question, in short

Venn diagram notation and shading, probability with letter cards and with students' subject preferences from given counts.

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

Part (ai) · 1 mark

Express the shaded overlap of A and B using set notation.

  1. 1Only the region in both A and B is shaded
  2. 2A ∩ B

AnswerA ∩ B

Part (aii) · 2 marks

Shade the region for Q ∪ P′ and the region for (K ∪ L) ∩ M′ in the two diagrams.

  1. 1Q ∪ P′: shade all of Q and everything outside P (leave only the part of P outside Q unshaded)
  2. 2(K ∪ L) ∩ M′: shade the parts of K and L that are not inside M

AnswerQ ∪ P′: everything shaded except the part of P outside Q (K ∪ L) ∩ M′: the parts of K and L that are outside M shaded

Part (bi) · 1 mark

From 11 letter cards, find the probability the chosen letter is not A.

  1. 12 cards show A, so 9 cards are not A
  2. 2P(not A) = 9/11

Answer9/11

Part (bii) · 3 marks

Two draws with replacement from the 11 cards; find the probability exactly one card shows N.

  1. 1P(N) = 2/11, P(not N) = 9/11
  2. 2P(exactly one N) = 2/11 × 9/11 + 9/11 × 2/11
  3. 3= 2 × 18/121 = 36/121

Answer36/121

Part (ci) · 2 marks

Fill in all regions of the Venn diagram using 50 students, 3 liking neither, 33 liking E, 42 liking M.

  1. 1Like at least one subject: 50 − 3 = 47
  2. 2E ∩ M = 33 + 42 − 47 = 28
  3. 3E only = 33 − 28 = 5, M only = 42 − 28 = 14
  4. 4Outside E and M: 3

AnswerE only: 5 E ∩ M: 28 M only: 14 Outside E and M: 3

Part (cii) · 1 mark

Find the probability a randomly chosen student likes both English and mathematics.

  1. 128 students like both
  2. 2P = 28/50

Answer28/50

Part (ciii) · 2 marks

Find the probability that two randomly chosen students both like mathematics.

  1. 1P = 42/50 × 41/49
  2. 2= 1722/2450 = 123/175

Answer123/175

Part (civ) · 2 marks

Given two students who like English are chosen, find the probability both also like mathematics.

  1. 128 of the 33 English students also like mathematics
  2. 2P = 28/33 × 27/32 = 756/1056
  3. 3= 63/88

Answer63/88

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Also searched as: 0580/41/M/J/22 · 0580_s22_qp_41 · 0580 s22 41 · question 8.
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