Use relative frequency (experimental probability) to estimate probabilities from data, understand how more trials improve the estimate, and calculate expected numbers of outcomes.

What this dot point is asking

The Eduqas probability content asks you to use relative frequency (experimental probability) to estimate a probability from collected data, to understand why a larger number of trials gives a better estimate, and to calculate expected numbers of outcomes. Where theoretical probability comes from counting equally likely outcomes, relative frequency comes from an experiment, which is essential when a spinner or dice is biased. It appears at both tiers, and the "how many would you expect" calculation is a dependable question, with the explanation of why more trials help being a common AO2 reasoning task.

Relative frequency

When outcomes are not equally likely, or you do not know the theoretical probability, you estimate it from an experiment.

So if a drawing pin lands "point up" $63$ times in $100$ drops, the relative frequency of "point up" is $\dfrac{63}{100} = 0.63$. This is an estimate of the true probability, which cannot be found by counting equally likely outcomes because the pin is not symmetrical.

Why more trials give a better estimate

The reliability of a relative-frequency estimate grows with the number of trials.

This is why, when comparing a spinner result over $20$ spins with one over $500$ spins, the larger experiment gives the better estimate. A good exam explanation must link the larger number of trials to the smaller effect of chance variation, not just assert that "more is better".

Expected outcomes

Once you have a probability, you can predict how many times an event should occur in a given number of trials.

The expected number is a prediction, not a certainty: you would expect about $50$ sixes, but any particular set of $300$ rolls might give a few more or fewer. The probability used can be theoretical (for a fair die) or a relative frequency (for a biased one).

Why this matters

Relative frequency is how probability is measured in the real world, from quality control to medical trials, where theoretical probabilities are unknown and must be estimated from data. Expected outcomes connect probability to prediction, which is the practical payoff of the whole topic. Because Eduqas asks you both to calculate and to explain (why more trials help, what an expected value means), clear reasoning alongside the arithmetic is essential for full marks.