Probability from many trials

Japanese school year: Junior high 1

What you learn

You will learn how the relative frequency of an event stabilizes around a constant value as an experiment is repeated many times. This forms the foundation for statistical estimation and modeling random phenomena. Prior familiarity with calculating ratios and interpreting frequency tables is beneficial.

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Key points

This formula finds the relative frequency $R$ of an event. Divide the number of times the event occurred ( $r$ ) by the total number of trials ( $n$ ).

R = \frac{r}{n}

This describes the law of large numbers. As the number of trials $n$ becomes very large, the relative frequency approaches a fixed theoretical probability.

This is an important consideration when estimating probability from data. If the number of trials is small, random fluctuations cause bias, requiring a large number of trials.

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Practice 1Coming soon