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4MA1/2HR Jun 2025, Question 14: Tree Diagrams for Independent Events

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 7 marks

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The question, in short

Complete a probability tree for beads drawn from bags A and B, find the chance of two reds, then include a box with green probability 2/11 and find the chance of more reds than greens.

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

Part (a) · 2 marks

Fill in all six branch probabilities on the tree diagram for bag A then bag B draws.

  1. 1Bag A has 5 + 4 = 9 beads: P(red) = 5/9, P(green) = 4/9
  2. 2Bag B has 7 + 3 = 10 beads: P(red) = 7/10, P(green) = 3/10
  3. 3The bag B probabilities are the same after red or green from bag A

AnswerBag A: red 5/9, green 4/9; Bag B (on both pairs of branches): red 7/10, green 3/10

Part (b) · 2 marks

Calculate the probability that both beads taken, one from each bag, are red.

  1. 1P(red, red) = 5/9 × 7/10
  2. 2= 35/90
  3. 3= 7/18

Answer7/18

Part (c) · 3 marks

Find the probability that among three beads drawn from A, B and the box, reds outnumber greens.

  1. 1P(red from box) = 1 − 2/11 = 9/11
  2. 2RRR = 5/9 × 7/10 × 9/11 = 315/990
  3. 3RRG = 5/9 × 7/10 × 2/11 = 70/990
  4. 4RGR = 5/9 × 3/10 × 9/11 = 135/990
  5. 5GRR = 4/9 × 7/10 × 9/11 = 252/990
  6. 6Total = 772/990 = 386/495

Answer386/495

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