Edexcel GCSE Mathematics Probability: a complete overview of the probability scale, tree and Venn diagrams and expected outcomes

What this content demands

Probability is where careful listing and clear logic pay off. Edexcel tests the probability scale, the AND and OR rules, tree diagrams (including the trickier without-replacement case), Venn diagrams with set notation, and the link between theory and experiment through relative frequency and expected outcomes.

This guide walks through the four areas and ties together the matching dot-point pages, each of which has its own practice questions.

Probability basics

Probability runs from $0$ to $1$, and for equally likely outcomes $P(A) = \dfrac{\text{favourable}}{\text{total}}$. All outcomes sum to $1$, so $P(\text{not A}) = 1 - P(A)$. Mutually exclusive events use the OR (add) rule; independent events use the AND (multiply) rule. Sample space diagrams list every outcome, making favourable ones easy to count.

Tree diagrams

A tree shows multi-stage events. Multiply along a path (AND), add between paths (OR). The branches at each stage sum to $1$. At Higher tier, without-replacement problems are conditional: the second set of branches changes because the first outcome alters what is left. The complement is the fast route for "at least one" questions.

Venn diagrams and set notation

A Venn diagram organises overlapping groups. The intersection $A \cap B$ is the overlap, the union $A \cup B$ is everything in either, and $A'$ is the complement. Fill from the overlap outwards to avoid double-counting. Probabilities come from counting a region over the total, and conditional probability $P(A \mid B)$ restricts the total to set $B$.

Relative frequency and expected outcomes

Relative frequency, $\dfrac{\text{successes}}{\text{trials}}$, estimates probability from data and improves with more trials. Comparing it with the theoretical value tests fairness. The expected number of outcomes is probability $\times$ number of trials.

Check your knowledge

A mix of probability questions across the four areas. Attempt them under timed conditions, then check against the solutions.

1. A fair die is rolled. Find the probability of an even number. (1 mark)
2. $P(\text{rain}) = 0.2$. Find $P(\text{no rain})$. (1 mark)
3. Find the probability of a head on a coin and a $3$ on a die. (2 marks)
4. A coin is flipped twice. Find the probability of two tails. (2 marks)
5. A bag has $4$ red and $6$ blue. Two are taken without replacement. Find the probability both are red. (3 marks)
6. In a class, $12$ like maths, $9$ like art, $4$ like both. How many like neither, out of $20$? (3 marks)
7. A spinner lands on red $48$ times in $200$ spins. Find the relative frequency of red. (2 marks)
8. $P(\text{win}) = 0.15$. Over $60$ games, how many wins are expected? (2 marks)