A Level Maths: Discrete Distributions (inc. Binomial Distribution) Topic Summary and Resources
Video Lessons
Watch alongside the worksheet for the full lesson experience, then test your understanding with the lesson questions.
Revision Notes
Handwritten notes summarising the key ideas for each lesson. Ideal for quick review before a test.
Exam Questions
Past-paper-style questions organised by topic, with full mark schemes.
Drawn from OCR and Edexcel past papers but designed to be useful for students of all UK exam boards — including AQA and OCR MEI — unless a sheet is explicitly board-specific.
Before You Start This Topic
It will help if you are confident with the following:
- Probability — basic probability and the multiplication rule for independent events
- Binomial Expansion — nCr coefficients are the binomial probabilities
- Indices — needed for raising probabilities to powers
A Level Maths discrete distributions introduces probability distributions for discrete random variables — random variables that take a finite or countable set of values. You learn to work with general discrete distributions, then focus on the binomial distribution, which is one of the most useful models in statistics and the basis for Binomial Hypothesis Testing.
You build probability tables for discrete random variables, check that probabilities sum to $1$, and use these to calculate probabilities of specific outcomes. You meet the discrete uniform distribution (every value equally likely). The main focus is the binomial distribution $X \sim B(n, p)$, which models the number of successes in $n$ independent trials, each with probability $p$ of success. You use your calculator to find individual binomial probabilities $P(X = r)$ and cumulative probabilities $P(X \le r)$. You translate phrases like 'at least 5', 'fewer than 3', 'more than 7' into the correct binomial calculation, and you model real situations using the binomial distribution, commenting critically on whether the assumptions (independence, constant probability) are appropriate.
Discrete distributions are part of the Statistics strand of A Level Maths for AQA, Edexcel, OCR, and OCR MEI students.
Watch out for…
A few things to be careful with: 'at least 5' means $P(X \ge 5) = 1 – P(X \le 4)$ — translate language to calculator-friendly form; the binomial assumes INDEPENDENT trials with CONSTANT probability — drawing cards WITHOUT replacement breaks both, so binomial is inappropriate there; 'between 3 and 7' is usually inclusive ($3$ to $7$) but check the question wording; and your calculator's cumulative binomial gives $P(X \le r)$, not $P(X < r)$ — for strict inequalities you may need to adjust.