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4024/12 May/Jun 2026, Question 8: Relative frequency

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 3 marks

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The question, in short

A 5-sided spinner (numbers 1 to 5) is spun 500 times, giving frequencies 105, 96, 95, 104, 100. Explain why it looks fair, find the relative frequency of a 5, and predict how many 5s to expect in 100 spins.

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

Part (a) · 1 mark

Explain why the results suggest the spinner is fair.

  1. 1A fair spinner would land on each number about 500 ÷ 5 = 100 times
  2. 2All the frequencies are close to 100, so the spinner is fair

AnswerThe frequencies are all close to 100 (500 ÷ 5)

Part (b) · 1 mark

Relative frequency of landing on 5.

  1. 1Relative frequency = 100/500
  2. 2= 1/5 = 0.2

Answer100/500 (accept 0.2 or 20%)

Part (c) · 1 mark

Expected number of 5s in 100 spins.

  1. 1Expected = 100 × 1/5
  2. 2= 20

Answer20

Stuck on a step? Read the free lesson: Relative Frequency and Expectation

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