AQA GCSE Statistics Probability: a complete overview of the rules, tree and Venn diagrams and distributions

What this module demands

Probability is about measuring and combining the chances of events. AQA tests the addition and multiplication rules, tree and Venn diagrams, conditional probability, and the main distributions including the binomial and expected value. Most marks come from setting out the working clearly and combining probabilities correctly.

This guide walks through the three topics in specification order, then sets out the exam patterns AQA repeats. Each topic has a matching dot-point page with practice questions; this overview ties them together.

Probability basics

The module opens with probability basics: the probability scale from $0$ to $1$, theoretical and experimental probability, relative frequency, expected frequency, and the addition and multiplication rules. Expected frequency, $P(\text{event}) \times \text{trials}$, is a standard calculation.

Tree and Venn diagrams

Tree diagrams and Venn covers sample space diagrams, tree diagrams (multiply along, add between), Venn diagrams with intersection, union and complement, and conditional probability, including "without replacement" problems.

Probability distributions

Probability distributions covers what a distribution is, the discrete uniform distribution, the binomial distribution, and expected value, $E(X) = \sum x \, P(x)$, the long-run average outcome.

How this module is examined

A typical AQA profile for this module:

• Basics. The scale, relative frequency, expected frequency and the two rules.
• Tree diagrams. Combined and "without replacement" probabilities.
• Venn diagrams. Intersection, union and complement with set notation.
• Distributions. The binomial and expected value calculations.

Check your knowledge

A mix of recall and calculation questions covering this module. Attempt them under timed conditions, then check against the solutions.

1. A bag has $3$ red and $7$ blue counters. Find the probability of a red. (1 mark)
2. A spinner lands red with probability $0.2$. In $50$ spins, how many reds are expected? (2 marks)
3. A coin and a die are used. Find the probability of a head and a six. (2 marks)
4. A bag has $4$ red and $6$ blue. Find the probability of two reds without replacement. (3 marks)
5. In a Venn diagram, what does $A \cap B$ represent? (1 mark)
6. A spinner scores $1$, $2$, $3$ with probabilities $0.5$, $0.3$, $0.2$. Find the expected score. (2 marks)
7. State the two conditions needed for a binomial distribution. (2 marks)
8. What is the largest possible value of a probability? (1 mark)