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4024/22 May/Jun 2020, Question 6: Basic Probability

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 10 marks

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The question, in short

From five numbered cards (5, 2, 4, 6, 3) two are picked and arranged side by side to form a two-digit number; also interpret Rowan's 200 dice throws shown in a bar chart.

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

Part (ai) · 1 mark

Work out the chance that the resulting two-digit number is below 30.

  1. 1There are 5 × 4 = 20 possible two-digit numbers
  2. 2Less than 30: 23, 24, 25, 26 (4 numbers)
  3. 3P = 4/20 = 0.2

Answer0.2 or 1/5

Part (aii) · 2 marks

Write down every two-digit number that can be made which is prime.

  1. 1Only numbers ending in 3 can be prime (others are even or end in 5): 23, 43, 53, 63
  2. 263 = 7 × 9 is not prime
  3. 323, 43, 53

Answer23, 43, 53

Part (aiii) · 2 marks

Work out the chance that the resulting two-digit number divides exactly by 4.

  1. 1Multiples of 4: 24, 32, 36, 52, 56, 64
  2. 2P = 6/20 = 0.3

Answer0.3 or 6/20

Part (bi) · 1 mark

Read the bar chart to fill in the missing frequencies for numbers 4, 5 and 6.

  1. 1From the bar chart: 4 → 35, 5 → 22, 6 → 38
  2. 2Check: 46 + 31 + 28 + 35 + 22 + 38 = 200

Answer35, 22, 38

Part (bii) · 2 marks

From Rowan's data, work out the relative frequency of throwing a value below 3.

  1. 1Less than 3: 46 + 31 = 77
  2. 2Relative frequency = 77/200

Answer77/200 or 0.385

Part (biii) · 2 marks

Give two reasons, based on the results, why the dice might not be fair.

  1. 1200 throws is a large sample, so the results should be reliable
  2. 2Expected frequency for each number = 200 × 1/6 ≈ 33
  3. 346/200 (for 1) is a lot bigger than 1/6, and 22/200 (for 5) is a lot smaller than 1/6

AnswerLarge sample; and 46/200 is a lot bigger than 1/6 or 22/200 is a lot smaller than 1/6

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