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4MA1/2H Jan 2019, Question 14: Tree Diagrams for Independent Events

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 5 marks

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The question, in short

Marcus plays two tennis games, each won with probability 0.35. Complete a two-stage probability tree and find the chance he wins at least one game.

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

Part (a) · 2 marks

Fill in the missing probabilities on the tree diagram for the first and second games, including the branches where Marcus does not win.

  1. 11 − 0.35 = 0.65
  2. 2Probability of not winning is 0.65
  3. 3Each branch for second game has 0.35 and 0.65

Answer0.65, 0.35, 0.65, 0.35, 0.65

Part (b) · 3 marks

Calculate the probability that Marcus wins one or both of the two games.

  1. 1P(lose a game) = 1 − 0.35 = 0.65
  2. 2P(lose both) = 0.65 × 0.65 = 0.4225
  3. 3P(win at least one) = 1 − 0.4225 = 0.5775

Answer0.5775

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