Expected frequency
Objective. Use probability to predict counts over repeated trials.
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- 2. Worked example
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Learn: the key idea
Expected frequency uses a known or theoretical probability to predict how many times an outcome should occur over a given number of trials, calculated by multiplying the probability by the number of trials. For example, if the probability of a spinner landing on blue is 1/4, then over 80 spins the expected frequency of blue is 1/4 × 80 = 20. This predicted figure is a theoretical estimate rather than a guaranteed exact result, since real experimental results can vary due to chance. Expected frequency is often compared with actual recorded results to judge whether a probability model, or the fairness of a device, seems accurate.
Worked example
The probability of a biased coin landing on heads is 0.35. Find the expected frequency of heads in 200 flips.
- 1Identify the probability of the outcome: 0.35.
- 2Identify the number of trials: 200.
- 3Multiply the probability by the number of trials: 0.35 × 200.
- 40.35 × 200 = 70.
Answer: 70
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Practice
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Start practisingCommon mistake. Pupils sometimes treat the expected frequency as an exact guaranteed outcome rather than a theoretical prediction, concluding a die is unfair just because the actual count differs slightly from the expected value. Expected frequency is a prediction, not a guarantee, so small differences from real results are normal.
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