Sample Space Listing

1) What you are listing

A sample space is the set of all possible outcomes of a chance experiment. In a listing exercise, your job is to write every outcome exactly once and in a clear format.

2) Build the list systematically

1. Identify the parts of the experiment that can vary.
2. Write the outcomes in an organized order, such as left-to-right or smallest-to-largest.
3. Combine each valid choice to form one outcome.
4. Keep going until every possible outcome has been included.

3) Simplify the final answer

If the answer can be written more cleanly, do so. Use braces for a set of outcomes, and separate each outcome with commas. Remove any repeated outcomes and make sure nothing impossible is included.

4) Check your work

A good check is to count the outcomes and compare them with how many should be possible from the experiment. Also make sure every outcome follows the rules of the situation and that no outcome appears twice.

5) Common mistakes to avoid

• Skipping an outcome.
• Listing the same outcome more than once.
• Mixing impossible outcomes into the sample space.
• Writing the answers in a confusing order.

A complete, simplified listing should be exhaustive, accurate, and easy to read.