The image represents a tree diagram where the first level has three branches labeled 1, 2, and 3. Each of these branches then splits into three further branches also labeled 1, 2, and 3. The diagram lists all possible combinations when choosing one number from the set {1, 2, 3} and then choosing another number from the same set. The problem asks us to list all possible outcomes.

1. Problem Description

The image represents a tree diagram where the first level has three branches labeled 1, 2, and

3. Each of these branches then splits into three further branches also labeled 1, 2, and

3. The diagram lists all possible combinations when choosing one number from the set {1, 2, 3} and then choosing another number from the same set. The problem asks us to list all possible outcomes.

2. Solution Steps

The tree diagram illustrates a sample space where we are choosing two numbers in sequence from the set {1, 2, 3}. The first number is represented by the first level of branching, and the second number is represented by the second level of branching. We can list the possible outcomes by following each path from the root of the tree to the end branches:

* Branch 1: 1-11, 2-12, 3-13 results in (1,1), (1,2), (1,3)

* Branch 2: 1-21, 2-22, 3-23 results in (2,1), (2,2), (2,3)

* Branch 3: 1-31, 2-32, 3-33 results in (3,1), (3,2), (3,3)

Therefore, the complete sample space is {(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)}.

3. Final Answer

The possible outcomes are (1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3).