Probability basics: how to calculate the chance of an event
Learn how to calculate probability, use 'not' events and find the probability of two events together, with worked examples for KS3 and GCSE.
KS3GCSEMiddle SchoolHigh SchoolCurriculum fit: GCSE Maths Probability (Foundation and Higher). US: Grade 7 and High School Statistics and Probability.
On this page
What is it?
Probability measures how likely an event is. It is a number from 0 (impossible) to 1 (certain), and can be written as a fraction, decimal or percentage.
When all outcomes are equally likely, the probability of an event is the number of favourable outcomes divided by the total number of outcomes.
Key formulas and ideas
- P(event) = favourable outcomes ÷ total outcomes.
- P(not A) = 1 − P(A).
- For independent events: P(A and B) = P(A) × P(B).
- Expected number of times = probability × number of trials.
Worked examples
Example 1: A fair die
Question: Find the probability of rolling an even number on a fair six-sided die.
- Even numbers: 2, 4, 6, which is 3 outcomes.
- Total outcomes: 6.
- P = 3 ÷ 6 = 1/2.
Answer: 1/2
Example 2: Not happening
Question: Find the probability of not rolling a 6.
- P(6) = 1/6.
- P(not 6) = 1 − 1/6 = 5/6.
Answer: 5/6
Example 3: Expected number
Question: A fair die is rolled 60 times. How many sixes are expected?
- P(6) = 1/6.
- Expected number = 60 × 1/6 = 10.
Answer: 10
Common mistakes
- Writing a probability greater than 1.
- Adding probabilities when they should be multiplied for 'and'.
- Counting outcomes that are not equally likely as if they were.
- Giving probabilities that do not add up to 1.
Practice questions
Frequently asked questions
Can a probability be greater than 1?
No. A probability of 1 means certain, and nothing can be more certain than that.
Does a probability of 1/2 mean it will happen once in every two tries?
No. It describes the long-run proportion, so the result of a small number of trials can differ.
Related guides
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GCSEHigh SchoolVenn diagrams and set notation: how to read and use them
Use sets, Venn diagrams and the symbols for union, intersection and complement to solve problems and find probabilities, with examples.
KS3GCSEMiddle SchoolHigh SchoolMean, median, mode and range: how to work them out
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KS3GCSEMiddle SchoolHigh SchoolSources and review
- DfE: GCSE mathematics subject content and assessment objectives
- Common Core State Standards: Mathematics (high school)
Reviewed by StudyMorrow editorial review on 5 Nov 2026.