Example Organized List:
lcl
V, V & & B, B
V, B & & B, V
Example Table:
Outcomes
Volleyball
Basketball
Volleyball
V, V
V, B
Basketball
B, V
B, B
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 (Junior) — Volleyball or Basketball
Second Choice (Senior) — Volleyball or Basketball
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 first choice of the sport to be played during the winter quarter are basketball (B) or volleyball (V). There are also two possible outcomes for the second choice, basketball (B) or volleyball (V). We will pair each possible outcome from the first choice with the possible outcomes from the second choice.
lcl
V, V & & B, B
V, B & & B, V
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
Volleyball
Basketball
Volleyball
V, V
V, B
Basketball
B, V
B, B
Tree Diagram
Let's now draw a tree diagram to represent the situation.
