8.2 Relative and Expected Frequencies

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1. What Is Probability? (A Quick Reminder)

Probability is a number that tells you how likely something is to happen. It is always a value between 0 and 1:

• 0 means the event is impossible (it will never happen).
• 1 means the event is certain (it will always happen).
• Values in between show how likely the event is — the closer to 1, the more likely.

For example, if you flip a fair coin, the probability of getting heads is 0.5 (or ½), because heads is equally as likely as tails.

2. Theoretical Probability vs. Experimental Probability

There are two ways to find a probability:

Theoretical probability — This is what you expect to happen based on equally likely outcomes. You calculate it using a formula, without doing any experiment.

For example, a spinner has 5 equal sections numbered 1 to 5. The theoretical probability of landing on 3 is 1 ÷ 5 = 0.2.

Experimental probability — This is what you observe actually happening when you carry out a real experiment or trial. It is also called relative frequency.

3. Relative Frequency — Probability from Experiments

When you actually carry out an experiment (like spinning a spinner, rolling a dice, or flipping a coin), you record the results. The relative frequency of an outcome is calculated from those real results.

Relative frequency is your best estimate of the true probability when you cannot work it out theoretically (for example, if you don't know whether a spinner is fair or biased).