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Statistics & Probability · Foundation & Higher

Relative frequency

Relative frequency (experimental probability) is calculated from the results of an experiment. As the number of trials increases, relative frequency gets closer to the true theoretical probability.

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Key facts to remember

  • 1Relative frequency = number of times event occurs ÷ total number of trials.
  • 2Relative frequency is an estimate of probability based on experiment.
  • 3Theoretical probability is based on equally likely outcomes (e.g. fair coin).
  • 4The more trials carried out, the more reliable the relative frequency estimate.
  • 5Relative frequency can be used when theoretical probability cannot be calculated.
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Formulas

Relative frequency
Relative frequency = frequency ÷ total trials
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Worked examples

Example 1

A biased coin is flipped 200 times. It lands on heads 130 times. Estimate the probability of heads.

Working

  1. Relative frequency = 130 ÷ 200 = 0.65
Answer0.65
Example 2

A die is rolled 300 times. The number 6 appears 42 times. Is the die likely to be fair?

Working

  1. Relative frequency of 6 = 42 ÷ 300 = 0.14
  2. Theoretical probability of 6 on a fair die = 1/6 ≈ 0.167
  3. 0.14 is below 0.167 but with 300 trials some variation is expected
  4. Cannot conclude the die is definitely biased without more evidence
Answer0.14; the die may or may not be biased — more trials are needed to be certain.
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Common mistakes

✗Treating relative frequency as exact probability — it is only an estimate.
✗Using too few trials to draw conclusions about bias.
✗Confusing relative frequency (experimental) with theoretical probability.
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Exam tips

✓Always state that relative frequency is an estimate of probability, not the exact probability.
✓More trials → more reliable estimate — mention this when asked about improving accuracy.

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