Pearson Edexcel International GCSE in Mathematics (Specification A) · 4MA1 · Free · no account needed
Probability
Fair counting, tree diagrams, and conditional probability — multiply along the branches, add between them.
Every lesson here ends the same way: learn it, teach it to an AI pupil who asks the awkward question, then defend it against the thinker with the strongest claim on it — free · no account needed.
3 modules of Pearson Edexcel International GCSE Mathematics (1 Higher Tier), each explained in full — what it is, why it works, when a question is asking for it, the mistakes that cost marks and worked examples — with five graded questions marked on your own device. Completely free.
The modules in Probability
Probability Basics
Probability as fair counting: single events, 'not' events, expected frequency and relative frequency — the foundations every tree diagram stands on. Probability measures likelihood from 0 (impossible) to 1 (certain).
When a question is asking for it: Spinners, dice, cards → count outcomes. Learn Probability Basics →
Combined Events & Tree Diagrams
Multiply along branches, add between them — with and without replacement, and the 'at least one' shortcut that saves whole minutes. A tree diagram maps a two-stage experiment: each path of branches is one storyline.
When a question is asking for it: Any two-stage random process. Learn Combined Events & Tree Diagrams →
Conditional Probability (Higher Tier)
Probability when you already know something — shrinking worlds, 'given that' questions, and combining branches over changing conditions. Higher Tier. P(B | A) — 'the probability of B given A' — is B's chance measured inside the world where A has already happened.
When a question is asking for it: The words 'given that…' or 'if it is known that…'; second-stage branches of no-replacement trees; two-way tables and Venn diagrams (the given event names the row/circle you're confined to). Learn Conditional Probability →
The mistakes that cost marks in Probability
One from each module — the error examiners see most, with the module that puts it right.
- Probabilities above 1 or given as '1 in 5' odds-style in an answer box. Probabilities are fractions/decimals in [0, 1]. (Probability Basics)
- Adding along a branch instead of multiplying (or getting a 'probability' bigger than 1 — the alarm bell for it). (Combined Events & Tree Diagrams)
- Using the whole total as the denominator: P(dog | cat) in the example is 6/15, not 6/50. The 'given' shrinks the world. (Conditional Probability)
Where Probability sits in the specification
Content area 6 of 4MA1, sub-topic 6.3. Incandio is aligned to the specification and is not published by Pearson; the numbers are given so you can check every module against your own copy.
- 6.3 — Probability — conditional probability (Higher)
How Probability is mastered on Incandio
Every module above ends the same way: five questions that climb Grade 6 → 9+, then you teach the method back to Ember, an AI pupil who asks the awkward question, and defend it against the mathematician with the strongest claim on it. Exam Ready carries 28 authored exam-style questions across this strand, marked on Incandio.
All of Incandio Mathematics · The 4MA1 specification · Exam Ready