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0580/42 Oct/Nov 2024, Question 8: Tree Diagrams for Dependent Events

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 8 marks

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The question, in short

Work with random selections from two bags: one holding 24 beads (10 yellow), the other holding 5 green, 6 white and 4 black marbles drawn without replacement.

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

Part (ai) · 1 mark

For the 24-bead bag, state the chance that a single random pick is yellow.

  1. 1P(yellow) = 10/24 = 5/12

Answer5/12

Part (aii) · 1 mark

For the same bag, state the chance that the picked bead is any colour other than yellow.

  1. 1P(not yellow) = 1 − 5/12 = 7/12

Answer7/12

Part (bi) · 2 marks

With 5 green, 6 white, 4 black marbles, find the chance the first pick is black and the next is white, without replacement.

  1. 1P(black then white) = 4/15 × 6/14
  2. 2= 24/210 = 4/35

Answer4/35

Part (bii) · 4 marks

For the same marble bag, work out the chance that the two marbles drawn without replacement differ in colour.

  1. 1P(same colour) = 5/15 × 4/14 + 6/15 × 5/14 + 4/15 × 3/14
  2. 2= (20 + 30 + 12)/210 = 62/210
  3. 3P(different colours) = 1 − 62/210 = 148/210 = 74/105

Answer74/105

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Also searched as: 0580/42/O/N/24 · 0580_w24_qp_42 · 0580 w24 42 · question 8.
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