Sample Space With a Tree Diagram

Sample space with a tree diagram

A tree diagram helps you list every possible outcome of a multi-step experiment. Each branch shows one choice at a step, and every complete path from start to finish represents one outcome in the sample space.

1) Read the steps in order

Identify what happens first, then second, and so on. For each step, write all possible results as branches from the current point.

2) Continue the branches

If a later step depends on an earlier one, draw the correct choices from each branch. If the choices stay the same, repeat the same set of branches each time.

3) List the outcomes

After the tree is complete, trace each full path and write the outcome as an ordered list or pair, using the order of the steps.

4) Simplify the final answer

If the question asks for the sample space, collect all distinct outcomes neatly. If it asks for the number of outcomes, count the complete paths.

5) Check your work

Make sure no path is missing and no outcome is repeated. A good check is to count the end branches and compare that number with your final list.

If probabilities are included, the tree also helps you attach them to each branch and organize the results clearly.