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4MA1/1H Jun 2019, Question 13: Tree Diagrams for Dependent Events

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

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The question, in short

Complete a probability tree for picking one child from group C (6 girls, 8 boys) and one from group D (3 girls, 7 boys), then find probabilities involving boys in one or two teams.

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

Part (a) · 2 marks

Fill in all branch probabilities on the tree diagram for group C and group D picks.

  1. 1From group C: 6 girls and 8 boys, so total 14 children. Probability of girl = 6/14, probability of boy = 8/14.
  2. 2From group D: 3 girls and 7 boys, so total 10 children. Probability of girl = 3/10, probability of boy = 7/10.

Answer6/14, 8/14, 3/10, 7/10

Part (b) · 2 marks

Calculate the probability that both selected children are boys.

  1. 1Probability of boy from group C = 8/14.
  2. 2Probability of boy from group D = 7/10.
  3. 3Multiply the two probabilities: (8/14) × (7/10) = 56/140.
  4. 4Simplify: 56 ÷ 28 = 2, 140 ÷ 28 = 5, so 2/5.

Answer2/5

Part (c) · 3 marks

After removing the first team, find the probability both teams contain two boys.

  1. 1First team: two boys. Probability = (8/14) × (7/10) = 56/140 = 2/5.
  2. 2After picking one boy from group C, 7 boys left out of 13 children.
  3. 3After picking one boy from group D, 6 boys left out of 9 children.
  4. 4Probability of two boys in second team = (7/13) × (6/9) = 42/117.
  5. 5Now multiply both probabilities: (2/5) × (42/117) = 84/585.
  6. 6Simplify: divide numerator and denominator by 3: 28/195.

Answer28/195

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