Use the probability scale from 0 to 1; calculate probabilities of single events from equally likely outcomes; use the fact that probabilities sum to 1; and list combined outcomes using sample space diagrams.

What this dot point is asking

OCR references P1 to P7 cover the foundations of probability: the $0$-to-$1$ scale, calculating single-event probabilities from equally likely outcomes, the fact that all probabilities sum to $1$, and listing combined outcomes with sample space diagrams. These ideas are the basis of every probability question, and they appear on every tier, often on the non-calculator paper where fractions must be handled by hand.

The probability scale

Every probability is a number between $0$ and $1$.

So an event with probability $\tfrac{1}{4}$ is unlikely but possible, and an event with probability $0.9$ is very likely. Words such as "impossible", "unlikely", "even chance", "likely" and "certain" map onto positions on this scale, and a question may ask you to place an event's probability with a cross on a $0$-to-$1$ line.

Single events from equally likely outcomes

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

So the probability of rolling an even number on a fair die is $\dfrac{3}{6} = \dfrac{1}{2}$ (three even faces out of six). For a bag of counters, the total is all the counters and the favourable count is those of the chosen colour. The assumption of "fair" or "at random" is what makes the outcomes equally likely, which the formula requires.

Probabilities sum to 1

The probabilities of all outcomes of an event add to $1$.

Because something must happen, the probabilities of all the mutually exclusive outcomes total $1$. This gives the useful complement rule: $P(\text{not } A) = 1 - P(A)$. So if the probability of rain is $0.3$, the probability of no rain is $0.7$. When a question lists probabilities for several outcomes and leaves one blank, the missing probability is $1$ minus the sum of the rest. This is a frequent two-step exam question.

Sample space diagrams

A sample space diagram lists every combined outcome.

For two events, a two-way grid shows all the outcomes. Rolling two dice gives a $6 \times 6$ grid of $36$ equally likely totals; flipping two coins gives four outcomes (HH, HT, TH, TT). Once every outcome is listed, counting the favourable ones and dividing by the total gives the probability. The diagram prevents missed or double-counted outcomes, which is why OCR rewards drawing it. Reading the wording precisely ("greater than" excludes the boundary, "at least" includes it) decides exactly which cells to count.

Why the basics matter

These foundations support tree diagrams, Venn diagrams and relative frequency, and they connect to the expected-outcomes idea used in modelling. OCR sets them in everyday contexts (dice, cards, spinners, bags) and rewards exact fractions, correct use of the complement rule, and complete sample spaces. Precision with the wording of an event is an AO2 skill that often separates full marks from partial ones.