Example Organized List:
lcl
F, B & & H, B
F, N & & H, N
Example Table:
Outcomes
Black
Navy blue
Flats
F, B
F, N
Heels
H, B
H, N
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 Choice (Type) — flats or heels
Second Choice (Color) — black or navy blue
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 all of them one at a time.
Organized List
The two possible outcomes for the choice of the type of shoes are flats (F) or heels (H). There are also two possible outcomes for the choice of color, black (B) or navy blue (N). We will pair each possible outcome from the first choice with the possible outcomes from the second choice.
lcl
F, B & & H, B
F, N & & H, N
Table
To make the table, we will list the outcomes of the first choice in the left column and the outcomes of the second choice in the top row.
Outcomes
Black
Navy blue
Flats
F, B
F, N
Heels
H, B
H, N
Tree Diagram
Let's now draw a tree diagram to represent the situation.
