The probability scale and notation, probabilities of single events, mutually exclusive and exhaustive events, the AND and OR rules for combined events, and listing outcomes using sample space diagrams.

What this dot point is asking

Edexcel expects you to use the probability scale and notation, find probabilities of single events, understand mutually exclusive and exhaustive events, combine events with the AND and OR rules, and list outcomes systematically using sample space diagrams. Probability rewards careful, organised listing and a clear sense of when to add and when to multiply.

The probability scale and notation

Every probability is a number between $0$ and $1$, written as a fraction, decimal or percentage.

So rolling a $4$ on a fair die has probability $\tfrac{1}{6}$, and rolling an even number has probability $\tfrac{3}{6} = \tfrac{1}{2}$. The complement rule is essential: the probability that an event does not happen is $1$ minus the probability that it does, so $P(\text{not a } 4) = 1 - \tfrac{1}{6} = \tfrac{5}{6}$.

Mutually exclusive and exhaustive events

Two events are mutually exclusive if they cannot both happen at once, such as rolling a $2$ and rolling a $5$ on one die. A set of events is exhaustive if together they cover every possibility.

This is why, in the exam question above, the three counter colours (the only possibilities) have probabilities summing to $1$.

The AND and OR rules

The two combining rules are the heart of probability, and choosing the right one is the key skill.

So the probability of rolling a $1$ OR a $2$ is $\tfrac{1}{6} + \tfrac{1}{6} = \tfrac{1}{3}$, while the probability of rolling a $6$ on one die AND a head on a coin is $\tfrac{1}{6} \times \tfrac{1}{2} = \tfrac{1}{12}$. A simple way to remember which is which: "or" widens the chance, so probabilities get bigger (you add), while "and" narrows it to a more specific outcome, so probabilities get smaller (you multiply two numbers below $1$).

Sample space diagrams

A sample space lists every possible outcome, making it easy to count favourable ones. For two dice, a $6 \times 6$ grid shows all $36$ equally likely outcomes, and you count those meeting the condition.

Try this

Q1. A fair die is rolled. Work out the probability of scoring a prime number. [2 marks]

• Cue. The primes on a die are $2, 3, 5$, so $\dfrac{3}{6} = \dfrac{1}{2}$.

Q2. The probability that a light is green is $0.7$. Work out the probability that it is not green. [1 mark]

• Cue. $1 - 0.7 = 0.3$.