Use relative frequency to estimate probability from experimental data, understand how estimates improve with more trials, identify bias, and calculate expected frequencies.

What this dot point is asking

Relative frequency estimates a probability from the results of an experiment, in contrast to the theoretical probability of equally likely outcomes. In the CCEA Probability content you must use relative frequency to estimate a probability, understand why the estimate improves with more trials, recognise when an experiment suggests bias, and calculate expected frequencies. These ideas connect probability to real data and to the idea of a fair test, and the expected-frequency calculation is a reliable mark.

Theoretical versus experimental probability

For a fair die or coin, you can work out the theoretical probability from equally likely outcomes: $P(\text{six}) = \tfrac{1}{6}$. But for a real, possibly biased, object, or for an event with no obvious symmetry, you estimate the probability by experiment instead. This estimate is the relative frequency.

Why more trials help

A relative frequency from only a few trials can be misleading; with more trials it settles down towards the true probability. This is the law of large numbers in everyday terms: the more times you repeat the experiment, the more reliable the estimate. So an estimate from 1000 spins is more trustworthy than one from 10 spins.

This is why exam answers should prefer the relative frequency from the largest number of trials when several experiments are given.

Recognising bias

If an object were fair, its relative frequencies would settle near the theoretical values. A relative frequency that stays clearly away from the expected value, over a large number of trials, suggests the object is biased.

For a fair die, each face should appear with relative frequency near $\tfrac{1}{6} \approx 0.17$. If, after many rolls, a six appears with relative frequency $0.30$, the die is likely biased towards six. The judgement must be based on enough trials, since a small experiment can stray from the expected value by chance.

Expected frequency

Once you have a probability (theoretical or estimated), you can predict how many times an event should occur in a number of trials.

Why this matters

Relative frequency links probability to real evidence, which is how probability is used in quality control, medicine and forecasting where theoretical values are unknown. The idea that more trials give a better estimate, and the test for bias, are exactly the AO2 and AO3 reasoning CCEA rewards, while the expected-frequency calculation is a dependable mark. Together they complete the probability content, connecting the theoretical methods to experimental data.