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4MA1/1HR Jan 2022, Question 13: Tree Diagrams for Independent Events

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 7 marks

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The question, in short

Complete a probability tree for two draws with replacement from a bag of 7 green and 5 red counters, find the probability both are red, then use a given probability to find the number of blue counters in a jar of 15.

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 counter drawn with replacement.

  1. 1First counter: P(Red) = 1 − 7/12 = 5/12
  2. 2The counter is put back, so the second draw has the same chances
  3. 3After Green: Green 7/12, Red 5/12; so the gaps are 5/12, 7/12, 5/12

Answer5/12, 7/12, 5/12

Part (b) · 2 marks

Calculate the probability that both counters drawn from the bag are red.

  1. 1P(First Red) = 5/12
  2. 2P(Second Red) = 5/12
  3. 3(5/12) × (5/12) = 25/144

Answer25/144

Part (c) · 3 marks

Given the probability that three counters of different colours are drawn is 7/24, work out how many blue counters the jar contains.

  1. 1Let x be the number of blue counters; Hector has no blue, so Meghan must take blue
  2. 2Hector must get one green and one red: 7/12 × 5/12 + 5/12 × 7/12 = 70/144
  3. 370/144 × x/15 = 7/24, which simplifies to 7x/216 = 7/24
  4. 4x = 216 ÷ 24 = 9

Answer9

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