Sample Space and Events
All outcomes and subsets of interest.
Key idea
All outcomes and subsets of interest.
In depth
The sample space S lists all possible outcomes; an event is a subset of S. Probability assigns a number to each event. Listing outcomes carefully avoids missing cases.
Worked example
Two coin flips: S = {HH, HT, TH, TT}. The event at least one head = {HH, HT, TH}.
Real-world uses
- Listing all possible outcomes of a board game move or a two-coin toss
Common mistake
Treating HT and TH as the same outcome.
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 Sample Space and Events?
All outcomes and subsets of interest. It is a topic at the intermediate level in Probability & Statistics.
Where is Sample Space and Events used in real life?
Real-world examples: Listing all possible outcomes of a board game move or a two-coin toss.
What should I learn before Sample Space and Events?
Make sure you are comfortable with Experiments of Chance, the previous topic in Probability & Statistics.
What is a common mistake with Sample Space and Events?
Treating HT and TH as the same outcome.
How can I practise Sample Space and 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 Sample Space and Events?
Move on to Basic Probability 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.