IGCSE Maths Probability Notes
Probability measures how likely an event is, from 0 (impossible) to 1 (certain). IGCSE combines this with tree diagrams and set notation.
Key concepts
- Probability scale
- All probabilities lie between 0 and 1, and a full set sums to 1.
- Combined events
- Multiply along branches (AND); add across outcomes (OR).
- Conditional probability
- Probabilities on the second branch may change (without replacement).
Key formulas
Single event
P(event) = favourable ÷ total
Complement
P(not A) = 1 − P(A)
Worked example
A bag has 3 red and 5 blue balls. Find P(red).
- 1Favourable outcomes: 3 red.
- 2Total outcomes: 3 + 5 = 8.
- 3P(red) = 3/8.
Answer: 3/8
Common mistakes
✗ Probabilities not summing to 1.
✓ Check all outcomes total 1.
✗ Adding when you should multiply.
✓ Multiply for 'and' (both happen); add for 'or'.
✗ Not adjusting for 'without replacement'.
✓ Reduce the total (and count) on the second pick.
Quick check
Try these, then reveal the answers.
P(even) on a fair die?Reveal answer
1/2
If P(win) = 0.3, P(not win)?Reveal answer
0.7
Multiply or add for two events both happening?Reveal answer
Multiply
Exam tips
- Write probabilities as fractions to keep working exact.
- Use the complement to shortcut 'at least one' questions.
- Track whether items are replaced between selections.
Related practice
Practise this topic
Exam-style questions with instant Gradion feedback.
Flashcards
Quick-fire recall to lock in the key facts.
Worksheets
Printable practice you can work through offline.
Past papers
Full papers with examiner-grade marking.
Gradion
Ask for a step-by-step explanation any time.
All Mathematics
Every Mathematics topic across every exam board.
Related topics
Frequently asked questions
What is the range of a probability?+
Between 0 (impossible) and 1 (certain); it can be written as a fraction, decimal or percentage.
When do I multiply probabilities?+
When you want two or more independent events to all happen ('and'), multiply their probabilities.
Create a free account to practise probability with Gradion feedback
Try 5 questions now, get instant examiner-grade marking and ask the Gradion to explain anything. Free during our early launch period — no credit card required.