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0580/31 Oct/Nov 2024, Question 6: Relative Frequency and Expectation

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 14 marks

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The question, in short

Recipe for 6 people scaled to 10; find milk, mass after 15% loss, temperature difference; factory tub rates; truck totals; complete relative frequency table and tree diagram probabilities.

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

Part (ai) · 2 marks

Scale the 270 ml milk from 6 to 10 people and state the amount needed.

  1. 1270 ÷ 6 × 10
  2. 2= 450 ml

Answer450

Part (aii) · 2 marks

Starting from 1100 g, reduce the mixture mass by 15% and find the new mass.

  1. 11100 × (1 − 15/100) = 1100 × 0.85
  2. 2= 935 g

Answer935

Part (aiii) · 1 mark

Find the temperature difference between 5°C and −18°C.

  1. 15 − (−18) = 23°C

Answer23

Part (bi) · 1 mark

Convert 25 920 tubs in 8 hours to tubs per minute.

  1. 18 hours = 8 × 60 = 480 minutes
  2. 225 920 ÷ 480 = 54

Answer54

Part (bii) · 1 mark

Multiply 6 tubs by 120 packs and 24 trays to find total tubs on the truck.

  1. 16 × 120 × 24 = 17 280

Answer17280

Part (ci) · 3 marks

Complete relative frequencies using chocolate three times banana, with all summing to 1.

  1. 1Chocolate + Banana = 1 − (0.34 + 0.18 + 0.12) = 0.36
  2. 2Chocolate : Banana = 3 : 1, so Banana = 0.36 ÷ 4 = 0.09
  3. 3Chocolate = 3 × 0.09 = 0.27

Answer| Chocolate | 0.27 | | Banana | 0.09 |

Part (cii) · 1 mark

Use the strawberry relative frequency to find expected strawberry sales out of 450.

  1. 10.18 × 450 = 81

Answer81

Part (ciiia) · 1 mark

Fill in the missing probabilities on the two-customer tree diagram.

  1. 1P(Child) = 1 − 0.7 = 0.3
  2. 2Each Child branch is 0.3

AnswerCorrect complete tree diagram: 0.3 0.3 0.3

Part (ciiib) · 2 marks

Find the probability that both the first and second customers are adults.

  1. 10.7 × 0.7 = 0.49

Answer0.49

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Also searched as: 0580/31/O/N/24 · 0580_w24_qp_31 · 0580 w24 31 · question 6.
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