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4MA1/1HR Jun 2018, Question 15: Tree Diagrams for Independent Events

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 8 marks

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The question, in short

Two bags, X with 20 counters (11 blue) and Y with 16 counters (9 blue), one counter drawn from each; complete a tree diagram and find probabilities of colour combinations.

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

Part (a) · 3 marks

Complete the probability tree diagram for drawing one counter from bag X and one from bag Y, filling in the missing branch probabilities.

  1. 1Bag X red = 20 − 11 = 9, so the red branch is 9/20
  2. 2Bag Y red = 16 − 9 = 7
  3. 3From each bag X branch draw a blue and a red branch
  4. 4Bag Y branches: blue 9/16, red 7/16

AnswerBag X: blue 11/20, red 9/20; Bag Y on both branches: blue 9/16, red 7/16

Part (b) · 2 marks

Calculate the probability that the counter drawn from bag X and the counter drawn from bag Y are both red.

  1. 1P(red from X) = 9/20
  2. 2P(red from Y) = 7/16
  3. 3(9/20) × (7/16) = 63/320

Answer63/320 or 0.196(875)

Part (c) · 3 marks

Calculate the probability that the two drawn counters are either both red or both blue.

  1. 1P(both red) = (9/20) × (7/16) = 63/320
  2. 2P(both blue) = (11/20) × (9/16) = 99/320
  3. 363/320 + 99/320 = 162/320

Answer162/320 or 0.506(25)

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