Example Organized List:
lcl
E, E & & I, I
E, I & & I, E
Example Table:
Outcomes
Ecuador
Italy
Ecuador
E, E
E, I
Italy
I, E
I, I
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 Year — Ecuador or Italy
Second Year — Ecuador or Italy
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 year abroad are Ecuador (E) or Italy (I). There are also two possible outcomes for the second year, Ecuador (E) or Italy (I). We will pair each possible outcome for the first year with the possible outcomes for the second year.
lcl
E, E & & I, I
E, I & & I, E
Table
To make the table, we will list the outcomes for the first year in the left column and the outcomes for the second year in the top row.
Outcomes
Ecuador
Italy
Ecuador
E, E
E, I
Italy
I, E
I, I
Tree Diagram
Let's now draw a tree diagram to represent the situation.
