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0580/43 Oct/Nov 2022, Question 7: Tree Diagrams for Dependent Events

Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 10 marks

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The question, in short

From six cards showing −3, −2, 2, 3, 5, 7, find probabilities for products of two cards drawn without replacement and for a sum of three cards.

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Part (ai) · 3 marks

Find the probability that multiplying the two chosen cards gives a score of 35.

  1. 1Score 35 needs 5 and 7
  2. 2P = 2 × 1/6 × 1/5
  3. 3= 1/15

Answer1/15

Part (aii) · 3 marks

Find the probability that the product of the two chosen cards is positive.

  1. 1Positive: both positive or both negative
  2. 2Both positive: 4/6 × 3/5 = 12/30
  3. 3Both negative: 2 × 1/6 × 1/5 = 2/30
  4. 4P = 14/30 = 7/15

Answer7/15

Part (b) · 4 marks

Find the probability that three cards drawn without replacement add to a total of 5.

  1. 1Total 5: cards −2, 2, 5 or −3, 3, 5
  2. 2Each set can be picked in 6 orders: 6 × 1/6 × 1/5 × 1/4 = 1/20
  3. 3P = 1/20 + 1/20 = 1/10

Answer1/10

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Also searched as: 0580/43/O/N/22 · 0580_w22_qp_43 · 0580 w22 43 · question 7.
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