Complementary Events
The chance something does not happen.
Key idea
The chance something does not happen.
In depth
The complement of E is "not E", with P(E′) = 1 − P(E). It is often easier to compute the chance something does not happen, especially for "at least one" problems.
Worked example
P(at least one six in 3 rolls) = 1 − (5/6)³ ≈ 0.421.
Formula
Real-world uses
- Working out the chance that at least one item is faulty, by finding the chance none are
Common mistake
Adding when you should be subtracting from 1.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Complementary Events?
The chance something does not happen. It is a topic at the intermediate level in Probability & Statistics.
What is the formula for Complementary Events?
The key formula is P(A′) = 1 − P(A).
Where is Complementary Events used in real life?
Real-world examples: Working out the chance that at least one item is faulty, by finding the chance none are.
What should I learn before Complementary Events?
Make sure you are comfortable with Probability Scale, the previous topic in Probability & Statistics.
What is a common mistake with Complementary Events?
Adding when you should be subtracting from 1.
How can I practise Complementary Events?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Complementary Events?
Move on to Experimental vs Theoretical next.
Related intermediate topics in Probability & Statistics
- Collecting Data and Sampling – Surveys, experiments and random sampling.
- Bias in Sampling – Systematic errors that make samples unrepresentative.
- Histograms – Bars showing frequency of numerical intervals.
- Dot Plots and Stem-and-Leaf Plots – Show the shape of small datasets.
- Mean – The arithmetic average.
- Median – The middle value of an ordered list.