The probability scale, theoretical and experimental probability, relative frequency, expected frequency, and the addition and multiplication rules.

What this dot point is asking

AQA wants you to use the probability scale, distinguish theoretical and experimental probability, use relative frequency and expected frequency, and apply the addition and multiplication rules to combine events. These ideas are the foundation for tree diagrams, Venn diagrams and probability distributions later in the module.

The probability scale

Because the total is always $1$, the probability of an event not happening is $1$ minus the probability that it does: $P(\text{not } A) = 1 - P(A)$. This complement rule is the quickest route to many marks, for example finding "at least one" by subtracting the probability of "none".

Theoretical and experimental probability

Theoretical probability applies when outcomes are equally likely (fair coins, dice, spinners). Experimental probability is used when they may not be, or when the mechanism is unknown, for example a possibly biased spinner or the chance of a bus arriving late. The law of large numbers says that as the number of trials grows, the relative frequency settles toward the true probability, which is why examiners reward the comment that "more trials give a more reliable estimate".

Expected frequency

Expected frequency converts a probability into a predicted count for a real number of trials. It is a long-run average, so the actual count varies around it: rolling that die $60$ times will rarely give exactly $10$ sixes, but repeated experiments will average close to $10$.

The addition and multiplication rules

"Mutually exclusive" means the events cannot both happen at once (rolling a $1$ or a $2$ on one die). "Independent" means one event does not change the probability of the other (a coin and a die). When events can overlap, the general addition rule subtracts the overlap: $P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$, which prevents double-counting outcomes in both events. Keeping these two ideas separate is essential: mutually exclusive is about whether events can co-occur (used for "or"), while independence is about whether one affects the other (used for "and"). A pair of events can be mutually exclusive but not independent, so do not assume one from the other.