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

OCR references P4 and P5 cover relative frequency (experimental probability) and expected outcomes: estimating a probability from data, understanding why more trials give a better estimate, and calculating how many times an outcome is expected. This content bridges theoretical probability and real data, and it underpins judging fairness. It appears on every tier and is often a two-part question combining an estimate with an expected count.

Relative frequency

Relative frequency estimates probability from an experiment.

So if a drawing pin lands point-up $35$ times in $50$ drops, the relative frequency of point-up is $\dfrac{35}{50} = 0.7$. There is no theoretical value here, because a pin is not symmetric, so the experiment is the only way to estimate the probability. Relative frequency can be written as a fraction, decimal or percentage.

Why more trials help

The estimate improves with more data.

The more trials you carry out, the closer the relative frequency tends to get to the true probability, a result sometimes called the law of large numbers. So an estimate from $1000$ spins is more trustworthy than one from $10$ spins. A graph of relative frequency against the number of trials typically swings widely at first and then settles towards a steady value. When a question asks which of several estimates is "most reliable", the answer is always the one from the largest number of trials, and the reason (more trials, closer to the true probability) earns a mark.

Judging fairness

Relative frequency reveals bias.

A fair (unbiased) object has equal theoretical probabilities, for example $\tfrac{1}{6}$ for each face of a die. If the relative frequency of an outcome settles clearly away from the theoretical value after many trials, the object is probably biased. So a die landing on six with relative frequency $0.25$ over $500$ rolls is biased towards six, because a fair die would settle near $0.167$. The judgement must be based on enough trials to be confident.

Expected outcomes

The expected number scales the probability up to many trials.

Why this matters

Relative frequency is how probability is estimated in the real world, from quality testing to sport, and OCR sets it in exactly such data contexts. The expected-number calculation is a direct, practical use of probability that also appears in fairness arguments and in checking model predictions against data. Choosing the largest sample for the best estimate, and justifying it, is the AO2 reasoning the board rewards.