Example Organized List:
lcl
O, O & & A, A
O, A & & A, O
Example Table:
Outcomes
Oil
Acrylic
Oil
O, O
O, A
Acrylic
A, O
A, A
Example Tree Diagram:
Practice makes perfect
We are given an experiment and want to represent the sample space by making an organized list, a table, and a tree diagram. The sample space of an experiment is the set of all possible outcomes. In this case, the sample space is the result of two stages.
First Project — Oil paints or acrylic paints
Second Project — Oil paints or acrylic paints
Keep in mind that there are several ways to make a list, a table, and a tree diagram. The part that matters most is that the sample space ends up with all of the possible combinations. We will make the list, the table, and the tree diagram one at a time.
Organized List
The two possible outcomes for the first project are oil (O) or acrylic (A). There are also two possible outcomes for the second project, oil (O) or acrylic (A). We will pair each possible outcome from the first project with the possible outcomes from the second project.
lcl
O, O & & A, A
O, A & & A, O
Table
To make the table, we will list the outcomes for the first project in the left column and the outcomes for the second project in the top row.
Outcomes
Oil
Acrylic
Oil
O, O
O, A
Acrylic
A, O
A, A
Tree Diagram
Let's now draw a tree diagram to represent the situation.
