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0580/42 May/Jun 2022, Question 6: Tree Diagrams for Dependent Events

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 13 marks

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The question, in short

Festival and match problems: estimate campers from a sample, find probability of different transport, reverse a percentage saving, and use bounds on counts and rates.

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

Part (a) · 2 marks

Use the 380 out of 500 sample proportion to estimate how many of the 55 300 festival-goers are camping.

  1. 1Estimate = 380/500 × 55 300
  2. 2= 0.76 × 55 300 = 42 028

Answer42 028

Part (b) · 4 marks

From 12 friends (5 car, 4 bus, 3 train), two chosen at random; find probability they use different transport types.

  1. 1P(same) = 5/12 × 4/11 + 4/12 × 3/11 + 3/12 × 2/11
  2. 2= (20 + 12 + 6)/132 = 38/132
  3. 3P(different) = 1 − 38/132 = 94/132 = 47/66

Answer47/66

Part (c) · 2 marks

A $43.68 student ticket saves 16% off full price; calculate the full price of a ticket.

  1. 143.68 is 100 − 16 = 84% of the full price
  2. 2Full price = 43.68 ÷ 0.84 = $52

Answer52

Part (di) · 3 marks

With 29 800 people (nearest 100) leaving at 400 per minute (nearest 50), find the lower bound for the minutes to empty.

  1. 1Lower bound of people = 29 800 − 50 = 29 750
  2. 2Upper bound of rate = 400 + 25 = 425 per minute
  3. 3Lower bound of time = 29 750 ÷ 425 = 70 minutes

Answer70 or 70.165… or 70.17 or 70.2

Part (dii) · 2 marks

Football 29 800 and cricket 27 500, both to nearest 100; find the upper bound of the difference in attendance.

  1. 1Upper bound of football = 29 850, lower bound of cricket = 27 450
  2. 2Upper bound of difference = 29 850 − 27 450 = 2400

Answer2399 or 2400

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