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4MA1/1H Jun 2024, Question 13: Tree Diagrams for Independent Events

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 5 marks

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The question, in short

Harman picks one bead at random from bag A (3 white, 7 black) and one from bag B (5 white, 4 black). Complete a probability tree and find the probability both beads are the same colour.

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

Part (a) · 2 marks

Fill in all the missing probabilities on the probability tree diagram for the two bags, using the bead counts given.

  1. 1On the first branch from Bag A, probability of white is 3 out of 10 beads, so write 3/10
  2. 2On the second branch from Bag A, probability of black is 7 out of 10 beads, so write 7/10
  3. 3From the white bead in Bag A, the chance of white from Bag B is 5 out of 9, so write 5/9
  4. 4From the white bead in Bag A, the chance of black from Bag B is 4 out of 9, so write 4/9
  5. 5From the black bead in Bag A, the chance of white from Bag B is 5 out of 9, so write 5/9
  6. 6From the black bead in Bag A, the chance of black from Bag B is 4 out of 9, so write 4/9

Answer3/10, 7/10, 5/9, 4/9, 5/9, 4/9

Part (b) · 3 marks

Calculate the probability that the two beads Harman takes are of the same colour.

  1. 1Probability of both white: (3/10) × (5/9) = 15/90
  2. 2Probability of both black: (7/10) × (4/9) = 28/90
  3. 3Add the two probabilities: 15/90 + 28/90 = 43/90
  4. 443/90

Answer43/90

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