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0580/42 Feb/Mar 2021, Question 4: Tree Diagrams for Dependent Events

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 9 marks

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The question, in short

Calculate expected voucher users in a larger group using a sample proportion, then find probabilities for hat colours when selecting students randomly.

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

Part (a) · 1 mark

Use the 28 out of 1000 rate to find expected users among 16 500 people.

  1. 128/1000 × 16 500 = 462

Answer462

Part (bi) · 1 mark

Find probability a randomly chosen student from 15 wears a red hat, given 7 red.

  1. 1P(red) = 7/15

Answer7/15

Part (bii) · 3 marks

Show the probability two randomly chosen students share the same hat colour equals 37/105.

  1. 1P(both red) = 7/15 × 6/14 = 42/210
  2. 2P(both green) = 6/15 × 5/14 = 30/210
  3. 3P(both white) = 2/15 × 1/14 = 2/210
  4. 4Total = 74/210 = 37/105

Answer7/15 × 6/14 + 6/15 × 5/14 + 2/15 × 1/14 = 37/105

Part (biii) · 4 marks

Find probability that at least two of three randomly chosen students wear red hats.

  1. 1P(RRR) = 7/15 × 6/14 × 5/13 = 210/2730
  2. 2P(exactly two red) = 3 × 7/15 × 6/14 × 8/13 = 1008/2730
  3. 3Total = 1218/2730
  4. 4= 29/65

Answer29/65

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Also searched as: 0580/42/F/M/21 · 0580_m21_qp_42 · 0580 m21 42 · question 4.
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