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0580/42 Feb/Mar 2022, Question 11: Tree Diagrams for Dependent Events

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 10 marks

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The question, in short

Complete a two-day probability tree for lateness with P(late)=1/6, then use a 50-student Venn diagram of glasses, trainers and mobile phones to answer set-notation, counting and probability questions.

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

Part (ai) · 2 marks

Fill in all six missing branch probabilities on the Monday and Tuesday tree diagram, using 1/6 for late.

  1. 1P(not late) = 1 − 1/6 = 5/6
  2. 2Write 1/6 on every Late branch and 5/6 on every Not late branch

Answer1/6 on all late branches 5/6 on all not late branches

Part (aii) · 2 marks

Find the probability Shalini is late on Monday and not late on Tuesday.

  1. 1P(late, not late) = 1/6 × 5/6
  2. 2= 5/36

Answer5/36

Part (bi) · 1 mark

Write set notation for the Venn region containing exactly one student.

  1. 1Only the region outside all three circles contains 1 student
  2. 2(G ∪ T ∪ M)′

Answer(G ∪ T ∪ M)′

Part (bii) · 1 mark

Calculate n(T′ ∩ (G ∪ M)) from the Venn diagram numbers.

  1. 1In G or M but not T: 0 + 19 + 9
  2. 2= 28

Answer28

Part (biii) · 1 mark

Find the probability a randomly chosen student wears trainers but not glasses.

  1. 1In T but not G: 3 + 14 = 17
  2. 2Probability = 17/50

Answer17/50

Part (biv) · 3 marks

For two students chosen at random from trainers wearers, find the probability both have mobile phones.

  1. 1Students wearing trainers: 2 + 3 + 2 + 14 = 21; of these with phones: 2 + 14 = 16
  2. 2P(both) = 16/21 × 15/20
  3. 3= 240/420 = 4/7

Answer4/7

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