Estimate probability from experimental data using relative frequency, understand how it stabilises with more trials, compare experimental with theoretical probability, and calculate expected frequencies.

What this dot point is asking

WJEC asks you to estimate probability from experimental data using relative frequency, to understand that relative frequency becomes a more reliable estimate as the number of trials increases, to compare experimental probability with the theoretical value, and to calculate expected frequencies by multiplying a probability by the number of trials. This is where probability meets real data: when outcomes are not equally likely (a biased dice, a drawing pin landing point up), experiment is the only way to estimate the probability. It is examined on both components and links to relative frequency in statistics.

Relative frequency

When you cannot reason out a probability, you estimate it by experiment.

So if a drawing pin lands point up $37$ times in $50$ drops, the relative frequency, and best estimate of the probability, is $\tfrac{37}{50} = 0.74$.

More trials, better estimate

Relative frequency settles down as the experiment grows.

This is why an estimate from $1000$ trials is trusted more than one from $10$ trials, and why WJEC asks which of several experiments gives the best estimate (the one with the most trials).

Comparing experimental and theoretical probability

For a fair object, the two should roughly agree.

When the theoretical probability is known (a fair coin is $\tfrac{1}{2}$), the experimental relative frequency should be close to it, and a big difference suggests the object is biased or the sample is small. When the object is biased, only the experimental relative frequency is available, so it must be used as the estimate rather than the fair-object value.

Expected outcomes

A probability predicts how often an event should occur in many trials.

Why this matters

Relative frequency and expected outcomes connect probability to real experiments and data, and they are the only way to handle biased objects where outcomes are not equally likely. The marks reward calculating relative frequency correctly, knowing that more trials give a better estimate, and computing expected frequencies by multiplying probability by the number of trials. The idea that "expected" is a prediction rather than a guarantee is a frequent reasoning point, and the topic links directly to relative frequency in the statistics strand.