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
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
Relative frequency of 6 = 42 ÷ 300 = 0.14
Theoretical probability of 6 on a fair die = 1/6 ≈ 0.167
0.14 is below 0.167 but with 300 trials some variation is expected
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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