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4MA1/2H Jun 2021, Question 13: Tree Diagrams for Independent Events

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 8 marks

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The question, in short

Given independent race win probabilities 0.7 and 0.4, fill in a tree diagram and find probabilities involving winning exactly one of two races and exactly two of three races.

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

Part (a) · 2 marks

Fill the missing branch probabilities on the two-race tree diagram, using that the two races are independent.

  1. 1First race: probability Emilie does not win is 1 − 0.7 = 0.3
  2. 2Second race, after winning first: probability she does not win is 1 − 0.4 = 0.6
  3. 3Second race, after not winning first: probability she wins is 0.4
  4. 4Second race, after not winning first: probability she does not win is 1 − 0.4 = 0.6

Answer0.3; 0.6, 0.4, 0.6

Part (b) · 3 marks

Calculate the probability that Emilie wins one race but not the other, out of the two races.

  1. 1Probability she wins first and not second: 0.7 × 0.6 = 0.42
  2. 2Probability she does not win first and wins second: 0.3 × 0.4 = 0.12
  3. 3Add these probabilities: 0.42 + 0.12 = 0.54

Answer0.54

Part (c) · 3 marks

Using the given third-race conditional probabilities 0.6 and 0.3, find the probability she wins exactly two of the three races.

  1. 1Probability she wins first two races: 0.7 × 0.4 = 0.28
  2. 2Then probability she loses third: 1 − 0.6 = 0.4
  3. 3So probability of win-win-lose: 0.28 × 0.4 = 0.112
  4. 4From (b), probability she wins exactly one of first two: 0.54
  5. 5Then probability she wins third: 0.3
  6. 6So probability of (exactly one win) and then win: 0.54 × 0.3 = 0.162
  7. 7Add both ways to win exactly two races: 0.112 + 0.162 = 0.274

Answer0.274

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