Pearson Edexcel International GCSE Mathematics · specification 4MA1 · Paper 1F | Whole paper: Number, Algebra, Geometry, Statistics · Free · no account needed
Probability (4MA1 specification)
Single events, combined events, tree diagrams, and the difference between with and without replacement.
Learn it on Incandio
The 3 Incandio pages that teach this — each explained in full, then proved in marked questions, taught back to an AI pupil and defended in a debate. Completely free.
- Probability Basics — Probability as fair counting: single events, 'not' events, expected frequency and relative frequency — the foundations every tree diagram stands on.
- Combined Events & Tree Diagrams — Multiply along branches, add between them — with and without replacement, and the 'at least one' shortcut that saves whole minutes.
- Conditional Probability — Probability when you already know something — shrinking worlds, 'given that' questions, and combining branches over changing conditions. Higher Tier.
The teaching route this belongs to: Probability — the lessons in order, with every gate.
Specification coverage
6 Statistics and probability — statements 6.5–6.9 (Foundation and Higher Tier)
Assessment objectives: AO3. Suggested learning time: 90 minutes.
Required knowledge
- Probability of a single event, and that probabilities sum to 1
- Relative frequency and expected frequency
- Combined events, and the use of tree diagrams and sample space diagrams
- Mutually exclusive and independent events
- Higher: conditional probability, including selections without replacement
Required skills
- Multiply along branches and add between branches on a tree diagram
- Adjust the second-stage denominators when there is no replacement
- Calculate expected frequency from a probability
How it is examined
- Structured questions building from a routine start to a multi-step finish
- Problem-solving questions with no method given
- 'Show that' and reasoning questions where the working IS the answer
Common mistakes
- Keeping the same denominator on the second stage of a without-replacement question. The total falls by one, and so does the count of whatever was taken.
- Adding along a branch instead of multiplying.
- Giving a probability greater than 1, which always signals that events have been added when they should have been multiplied.
- Forgetting that 'at least one' is usually fastest as 1 − P(none).
This page maps the specification. The pages above teach it, and the Mathematics modules hold the whole course — completely free.