The probability scale, equally likely outcomes, the fact that probabilities sum to one, and combining mutually exclusive and independent events.

What this dot point is asking

AQA wants you to measure probability on a $0$ to $1$ scale, use equally likely outcomes and sample spaces, apply the fact that all probabilities sum to $1$, and combine events with the addition rule (for mutually exclusive events) and the multiplication rule (for independent events). These foundations feed directly into tree diagrams, Venn diagrams and relative frequency, so getting the AND/OR rules right here pays off throughout the strand.

The probability scale and equally likely outcomes

Every probability is a number between $0$ and $1$, often written as a fraction, decimal or percentage. An impossible event has probability $0$, a certain one has probability $1$, and an even chance is $0.5$.

Rolling a fair dice, the probability of an even number is $\tfrac{3}{6} = \tfrac{1}{2}$, because three of the six equally likely outcomes ($2, 4, 6$) are favourable. A sample space lists all possible outcomes; for two dice it is a $6 \times 6$ grid of $36$ outcomes, which lets you count favourable cases for events such as "total of $7$".

Probabilities sum to one

For a set of outcomes that covers every possibility exactly once (an exhaustive, mutually exclusive set), the probabilities add to $1$. This gives the complement rule: the probability that an event does not happen is $1$ minus the probability that it does. If the probability of rain is $0.3$, the probability of no rain is $0.7$. This also lets you find a missing probability, as in a spinner where the known sectors must leave the rest to sum to $1$.

Combining events: the addition and multiplication rules

Expected frequency

Multiplying a probability by the number of trials gives the expected frequency. If a biased coin lands heads with probability $0.6$, then in $50$ flips you expect about $0.6 \times 50 = 30$ heads. This is an estimate, not a guarantee, and it links to relative frequency.

Listing outcomes systematically

Many probability questions hinge on counting outcomes correctly, so a systematic listing method matters. For two events, a sample-space grid (a table with one event along the top and the other down the side) shows every combination at once, such as the $36$ totals from two dice. For choosing items, list combinations in a fixed order so none are missed or repeated: the ways to pick two letters from A, B, C are AB, AC, BC. A disciplined, ordered list is what separates a full-mark answer from one that misses cases, and examiners reward clear systematic working.

The probability of the complement

The complement rule, $P(\text{not } A) = 1 - P(A)$, is one of the most useful tools because it is often far easier to find the probability that something does not happen. To find the probability of "at least one" event across several trials, compute the probability of "none" and subtract from $1$. For example, the probability of rolling at least one six in two rolls of a fair dice is easier as $1 - \left(\tfrac{5}{6}\right)^2 = 1 - \tfrac{25}{36} = \tfrac{11}{36}$ than by adding up all the favourable cases. Recognising when the complement is the quicker route is a valuable exam habit.