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4MA1/1H Jun 2022, Question 12: Tree Diagrams for Dependent Events

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

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The question, in short

Rudolf visits a gym; given treadmill use probability 0.8 and cross trainer probabilities 0.3 with treadmill and 0.6 without, fill a two-stage tree and find the joint probability for both activities.

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

Part (a) · 2 marks

Fill in the six missing branch probabilities on the tree diagram, covering treadmill use or non-use followed by cross trainer use or non-use.

  1. 1Probability of using treadmill is given as 0.8
  2. 2So probability of not using treadmill is 1 − 0.8 = 0.2
  3. 3Given he uses treadmill, probability of using cross trainer is 0.3
  4. 4So probability of not using cross trainer (given treadmill) is 1 − 0.3 = 0.7
  5. 5Given he does not use treadmill, probability of using cross trainer is 0.6
  6. 6So probability of not using cross trainer (given no treadmill) is 1 − 0.6 = 0.4

Answer0.8, 0.2, 0.3, 0.7, 0.6, 0.4

Part (b) · 2 marks

Calculate the probability that Rudolf does the treadmill and the cross trainer.

  1. 1Probability of using both treadmill and cross trainer is
  2. 2P(treadmill) × P(cross trainer | treadmill)
  3. 30.8 × 0.3 = 0.24

Answer0.24

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