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4MA1/2H Jun 2018, Question 13: Tree Diagrams for Dependent Events

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

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The question, in short

Felix picks two cards from 10 (5 red, 4 blue, 1 green) without replacement; fill in the tree's second-branch probabilities and find the chance of at least one blue and no green.

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 second set of branches of the tree diagram.

  1. 1After taking a red card first, 4 red, 4 blue, 1 green remain: probabilities are 4/9, 4/9, 1/9
  2. 2After taking a blue card first, 5 red, 3 blue, 1 green remain: probabilities are 5/9, 3/9, 1/9
  3. 3After taking a green card first, 5 red, 4 blue, 0 green remain: probabilities are 5/9, 4/9, 0

Answer4/9, 4/9, 1/9, 5/9, 3/9, 1/9, 5/9, 4/9, 0

Part (b) · 3 marks

Calculate the probability that the two cards include one or more blue cards and zero green cards.

  1. 1Probability of red then blue: 5/10 × 4/9 = 20/90
  2. 2Probability of blue then red: 4/10 × 5/9 = 20/90
  3. 3Probability of blue then blue: 4/10 × 3/9 = 12/90
  4. 4Add the three outcomes: 20/90 + 20/90 + 12/90 = 52/90

Answer52/90

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