# Relative frequency

An estimate of probability from an experiment: the number of times something happened divided by the total number of trials.

Maths (school) · Part 08: Probability and statistics · Card 2 of 8 · Last updated 2026-10-19

## Analogy

Like judging a weather pattern from last year's records.

## Example

**18 reds in 60 spins**

Relative frequency = 18 / 60 = 0.3
In 200 spins, expect
0.3 x 200 = 60 reds

## In practice

Insurance firms use past records as relative frequencies to guess future risk.

## Practice

### Flashcards

- **18 reds in 60 spins. What is the relative frequency of red?** 0.3 (18 / 60).

## Questions people ask

### Why do more trials give a better estimate?

With few trials, luck can distort the results. With many trials, the relative frequency settles closer to the true probability. Flipping a coin 10 times might give 7 heads, but 1,000 flips will give close to 500. This idea is sometimes called the law of large numbers, and it is why casinos and insurers depend on big samples.

### How do you predict how many times something will happen?

Multiply the probability by the number of trials. If the probability of red is 0.3 and you spin 200 times, you expect 0.3 x 200 = 60 reds. It is an estimate, not a guarantee. The more trials there are, the closer the actual number usually gets to your expected value.

## Related concepts

- [Probability scale](https://studyvisually.com/learn/science/maths-school/maths-school-part-8/maths-school-part-8-concept-1)
- [Mutually exclusive events](https://studyvisually.com/learn/science/maths-school/maths-school-part-8/maths-school-part-8-concept-3)
- [Independent events](https://studyvisually.com/learn/science/maths-school/maths-school-part-8/maths-school-part-8-concept-4)
- [Tree diagrams](https://studyvisually.com/learn/science/maths-school/maths-school-part-8/maths-school-part-8-concept-5)

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