Knowledge organisers

Probability: A Level Maths knowledge organiser

Everything to know about probability on one page: key definitions, the formulas, a worked example, the mistakes to avoid and a checklist of what you should be able to do.

Download the A4 sheet (PDF)

Key definitions

Mutually exclusive: Events that cannot both happen: P(A ∩ B) = 0.
Independent: One event does not change the chance of the other: P(A ∩ B) = P(A)P(B).
Conditional probability: P(A | B) = P(A ∩ B)/P(B), the chance of A once B is known.
Venn diagram: Overlapping regions show events; fill in the intersection first.

Key formulas

Formulas marked with a label are given in the exam (we only say so where our formula sheet confirms it). Learn the rest.

UnionIn the formula booklet: Edexcel, AQA, OCR	\(P(A\cup B)=P(A)+P(B)\) \(-P(A\cap B)\)
IntersectionIn the formula booklet: Edexcel, AQA, OCR	\(P(A\cap B)=P(A)\times P(B\mid A)\)
ConditionalIn the formula booklet: Edexcel, OCR	\(P(A\mid B)=\frac{P(A\cap B)}{P(B)}\)
IndependentIn the formula booklet: Edexcel	\(P(A\cap B)=P(A)P(B),\) \(P(A\mid B)=P(A)\)

Worked example

P(A) = 0.4, P(B) = 0.5 and P(A ∩ B) = 0.2. Are A and B independent? Find P(A ∪ B).

P(A) × P(B) = 0.4 × 0.5 = 0.2 = P(A ∩ B)
P(A ∪ B) = 0.4 + 0.5 − 0.2

Answer: Yes, they are independent; P(A ∪ B) = 0.7

Common mistakes

Correlation read as causation
Extrapolation without comment
'independent' confused with 'mutually exclusive'
Log y = log a + x log b read as gradient a

More on what examiners see students get wrong: Examiner Insights.

You should be able to…

Calculate probabilities from sample spaces and use Venn diagrams with two or three events to find probabilities of unions, intersections and complements.
Use the addition rule for mutually exclusive events and the multiplication rule for independent events, and test whether two events are independent.
Use set notation, including unions, intersections and complements, to describe events and calculate probabilities from Venn diagrams.
Calculate conditional probabilities such as P(A | B) from two-way tables and descriptions, and use them to decide whether events are independent.
Use the formulae P(A ∪ B) = P(A) + P(B) − P(A ∩ B) and P(A ∩ B) = P(A | B)P(B) to solve probability problems.
Use tree diagrams and two-way tables to find conditional probabilities, including working backwards to find the probability of an earlier event.

The printable sheet

Probability knowledge organiser for A Level Maths: one A4 page of key definitions, formulas, a worked example and common mistakes — Probability knowledge organiser (A Level Maths), A4. Download the PDF.

Revise it next

Other A Level Maths topics: Proof · Algebra and functions · Coordinate geometry · Sequences and series · Trigonometry · Exponentials and logarithms · Differentiation · Integration · Numerical methods · Vectors · Sampling and data · Binomial and normal distributions · Hypothesis testing · Kinematics · Forces and Newton's laws · Moments · All A Level Maths organisers