Use the probability scale from 0 to 1, find probabilities of single events, use that probabilities sum to 1, apply the mutually exclusive addition rule, and list outcomes with sample space diagrams.

What this dot point is asking

Probability measures how likely an event is, and this is the foundation of the CCEA Handling Data strand's probability content. You must use the probability scale from 0 to 1, find the probability of a single event, use that all the probabilities sum to 1, apply the addition rule for mutually exclusive events, and list outcomes systematically using sample space diagrams. These ideas appear at both tiers and underpin the Higher-tier tree and Venn diagram work.

The probability scale

Every probability is a number from 0 to 1. A probability of 0 means the event is impossible, 1 means it is certain, and $\tfrac{1}{2}$ means it is as likely as not. Probabilities can be written as fractions, decimals or percentages, and you should be able to move between them. Placing events on this scale, and ordering them by likelihood, is a basic exam skill.

Single-event probability

When outcomes are equally likely, probability is a simple fraction.

Probabilities sum to 1

For a complete set of outcomes (every possible result), the probabilities always add up to 1. This gives the useful complement rule.

The complement rule often turns a hard "at least one" calculation into an easy "none" calculation, which is a powerful shortcut.

Mutually exclusive events and the addition rule

Two events are mutually exclusive if they cannot both happen at the same time, such as rolling a 2 or rolling a 5 on one die. For mutually exclusive events the probabilities simply add.

So $P(A \text{ or } B) = P(A) + P(B)$ when $A$ and $B$ cannot both occur. The probabilities of a full set of mutually exclusive outcomes add to 1, which is how you find a missing probability, as in the spinner question.

Sample space diagrams

A sample space diagram lists every possible outcome, making it easy to count favourable ones. For two events, such as throwing two dice, a grid shows all the combinations.

Why this matters

Probability is how mathematics measures uncertainty, used in risk, games, insurance and science, and these basics are the foundation for the Higher-tier tree and Venn diagram methods. The complement rule and the addition rule are reused constantly, and systematic listing with sample spaces prevents the miscounting that loses marks. CCEA expects probabilities written clearly as fractions, decimals or percentages, and a quick sense-check that they lie between 0 and 1.