Example Organized List:
lcl
S, NB & & M, NB & & L, NB
S, B & & M, B & & L, B
S, EB & & M, EB & & L, EB
Example Table:
Outcomes
No Butter
Butter
Extra Butter
Small
S, NB
S, B
S, EB
Medium
M, NB
M, B
M, EB
Large
L, NB
L, B
L, EB
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. The sample space is the result of choosing one out of three popcorn sizes and one out of three butter options.
First Choice (Size) — small or medium or large
Second Choice (Butter) — no butter or butter or extra butter
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 three possible outcomes for the choice of the popcorn size are small (S), medium (M) or large (L). There are also three possible outcomes for the choice of the butter - no butter (NB), butter (B) or extra butter (EB). We will pair each possible outcome from the first choice with the possible outcomes from the second choice.
lcl
S, NB & & M, NB & & L, NB
S, B & & M, B & & L, B
S, EB & & M, EB & & L, EB
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
No Butter
Butter
Extra Butter
Small
S, NB
S, B
S, EB
Medium
M, NB
M, B
M, EB
Large
L, NB
L, B
L, EB
Tree Diagram
Let's now draw a tree diagram to represent the situation.
