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4024/22 Oct/Nov 2024, Question 5: Tree Diagrams for Dependent Events

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 6 marks

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The question, in short

From nine cards numbered 1, 1, 2, 2, 2, 5, 6, 7, 8, work out probabilities for drawing cards with and without replacement.

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

Part (a) · 1 mark

One card drawn and replaced; find the probability it shows an odd number.

  1. 1Odd numbers: 1, 1, 5, 7
  2. 2P(odd) = 4/9

Answer4/9

Part (b) · 2 marks

Two cards drawn with replacement; find the probability both show the number 1.

  1. 1P(1) = 2/9 each time
  2. 2P(both 1) = 2/9 × 2/9 = 4/81

Answer4/81

Part (c) · 3 marks

Two cards drawn without replacement; find the probability their product is less than 5.

  1. 1A product less than 5 needs both cards from 1, 1, 2, 2, 2 (1 × 1, 1 × 2, 2 × 2); any card 5 or more gives a product of at least 5
  2. 2P = 5/9 × 4/8 = 20/72
  3. 3= 5/18

Answer5/18

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