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4024/22 May/Jun 2024, Question 2: Combined Events with Two-Way Tables

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 7 marks

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The question, in short

Use a fair 1 to 5 pentagonal spinner to work out single-spin probabilities, complete a two-spin sum table, and find probabilities of totals.

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

Part (ai) · 1 mark

Find the probability that one spin gives a score of 3.

  1. 1One 3 out of 5 equally likely numbers: 1/5

Answer1/5

Part (aii) · 1 mark

Find the probability that one spin gives an even score.

  1. 1Even: 2 and 4, so 2/5

Answer2/5

Part (bi) · 2 marks

Complete the two-spin addition table for all pairs of scores 1 to 5.

  1. 1Each entry = first spin + second spin
  2. 2Row 3: 4, 5, 6, 7, 8
  3. 3Row 4: 5, 6, 7, 8, 9
  4. 4Row 5: 6, 7, 8, 9, 10

Answer| 3 | 4 | 5 | 6 | 7 | 8 | | 4 | 5 | 6 | 7 | 8 | 9 | | 5 | 6 | 7 | 8 | 9 | 10 |

Part (bii) · 1 mark

Using the completed table, find the probability that the total is 4.

  1. 1There are 5 × 5 = 25 equally likely pairs of scores
  2. 2Pairs that add to 4: (1, 3), (2, 2), (3, 1), so 3 pairs
  3. 3P(total 4) = 3/25

Answer3/25

Part (biii) · 2 marks

Using the completed table, find the probability that the total exceeds 6.

  1. 1Two spins give 5 × 5 = 25 equally likely outcomes.
  2. 2Totals over 6: 7 (4 ways), 8 (3 ways), 9 (2 ways), 10 (1 way)
  3. 3That is 10 outcomes, so P = 10/25

Answer10/25

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Also searched as: 4024/22/M/J/24 · 4024_s24_qp_22 · 4024 s24 22 · question 2.
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