Example Organized List:
lcl
R, S & B, S & Y, S & G, S & P, S & O, S
R, L & B, L & Y, L & G, L & P, L & O, L
Example Table:
Outcomes
Short-sleeved
Long-sleeved
Red
R, S
R, L
Blue
B, S
B, L
Yellow
Y, S
Y, L
Green
G, S
G, L
Pink
P, S
P, L
Orange
O, S
O, L
Example Tree Diagram:
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 choosing one out of six shirt colors and one out of two sleeve lengths.
First Choice (Color) — red, blue, yellow, green, pink, or orange
Second Choice (Sleeve) — short-sleeved or long-sleeved
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 the list, the table, and the tree diagram one at a time.
Organized List
The six possible outcomes for the choice of the shirt color are red (R), blue (B), yellow (Y), green (G), pink (P), or orange (O). There are two possible outcomes for the choice of the sleeve length - short-sleeved (S) or long-sleeved (L). We will pair each possible outcome from the first choice with the possible outcomes from the second choice.
lcl
R, S & B, S & Y, S & G, S & P, S & O, S
R, L & B, L & Y, L & G, L & P, L & O, L
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
Short-sleeved
Long-sleeved
Red
R, S
R, L
Blue
B, S
B, L
Yellow
Y, S
Y, L
Green
G, S
G, L
Pink
P, S
P, L
Orange
O, S
O, L
Tree Diagram
Let's now draw a tree diagram to represent the situation.
