Example Organized List:
lcl
S, S & & N, N
S, N & & N, S
Example Table:
Outcomes
Smithsonian
Natural
Smithsonian
S, S
S, N
Natural
N, S
N, 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 Class — Smithsonian or Museum of Natural History
Second Class — Smithsonian or Museum of Natural History
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 trip destination of the first class are the Smithsonian (S) or the Natural (N). There are also two possible outcomes for the second class, the Smithsonian (S) or the Natural (N). We will pair each possible outcome for the first class with the possible outcomes from the second class.
lcl
S, S & & N, N
S, N & & N, S
Table
To make the table, we will list the outcomes for the first class in the left column and the outcomes for the second class in the top row.
Outcomes
Smithsonian
Natural
Smithsonian
S, S
S, N
Natural
N, S
N, N
Tree Diagram
Let's now draw a tree diagram to represent the situation.
