Fiducia TogetherProbability
How likely something is, on a scale from 0 to 1. Trees, tables and the difference between with and without replacement.
Please note: This page explains a word or a process in education. It is general information about the system, the law and the guidance in England — not advice about your child, your school or your exam. If a decision is going against you, get advice from one of the free services we link to before you agree to anything or miss a deadline. If you are revising, check your own exam board's specification: boards word things differently and yours is the one that marks you.
What it is
Probability is the number of favourable outcomes over the total number of outcomes, expressed as a fraction, decimal or percentage between 0 and 1.
Where it applies
Both tiers. Higher adds conditional probability and Venn diagram notation.
How it works
For combined events, a tree diagram multiplies along branches and adds between them. Sample space diagrams handle two events with small outcome sets.
Without replacement changes the second probability because the total has shrunk — that is the distinction the exam tests.
How to use it in your work
Probabilities of all outcomes sum to 1, which is the fastest way to find "at least one" — take 1 minus the probability of none.
Label tree branches with the probabilities AND the outcomes. Unlabelled trees lose method marks.
Leave answers as fractions unless told otherwise; rounding early goes wrong.
Where to get help
Your teacher, your board's specification for what is on your paper, and Bitesize for worked examples. The maths song runs the topics in order.
Revise this with a song
These are ours. We write revision songs because a lot of people remember a tune when they cannot remember a page, and because revising out loud in the kitchen beats staring at a highlighter.
- The Maths Song The GCSE maths topics, in order.
Where to read more
Last reviewed 2026-08-28 by Fiducia Together · Next review due 2027-08-28
Please note: This page explains a word or a process in education. It is general information about the system, the law and the guidance in England — not advice about your child, your school or your exam. If a decision is going against you, get advice from one of the free services we link to before you agree to anything or miss a deadline. If you are revising, check your own exam board's specification: boards word things differently and yours is the one that marks you.