The idea

Relative frequency & expected outcomes

Estimating a probability from data — relative frequency is frequency divided by the number of trials — why more trials sharpen the estimate, how to test a dice or spinner for bias, and why the expected number is probability times trials.

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Probability · Basic probability

Relative frequency & expected outcomes

Why it works

When there is nothing to calculate, measure

A fair dice has six equally likely faces, so

P(\text{six}) = \frac{1}{6}

— no experiment needed. But bend the dice, or drop a drawing pin, and there is no symmetry to argue from. The only way in is to watch what actually happens:

\text{relative frequency} = \frac{\text{number of times the outcome happened}}{\text{total number of trials}}.

Drop a pin

200

times, see point-up

130

times, and the relative frequency is

\frac{130}{200} = 0.65

. A part over a whole, it lands between

0

and

1

like any probability — and across all outcomes it totals

1

, because every trial produced exactly one of them.

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