Example Organized List:
lcl
H, P & & H, R & & H, S & & H, T & & H, H
S, P & & S, R & & S, S & & S, T & & S, H
Example Table:
Outcomes
Rhombus
Square
Parallelogram
H, P
S, P
Rectangle
H, R
S, R
Square
H, S
S, S
Trapezoid
H, T
S, T
Rhombus
H, H
S, H
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 choices of quadrilaterals. One of them has to have sides of equal length.
Now, we know that the first quadrilateral can be either a rhombus or a square.
The second quadrilateral must have at least one set of parallel sides.
Finally, we know the possible outcomes for each choice of the quadrilateral.
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 two possible outcomes for the choice of the first quadrilateral are a rhombus (H) or a square (S). There are five possible outcomes for the choice of the second quadrilateral, parallelogram (P), rectangle (R), square (S), trapezoid (T) or rhombus (H). We will pair each possible outcome for the first quadrilateral with the possible outcomes for the second quadrilateral.
lcl
H, P & & H, R & & H, S & & H, T & & H, H
S, P & & S, R & & S, S & & S, T & & S, H
Table
To make the table, we will list the outcomes of the choice of the first quadrilateral in the left column and the outcomes of the second quadrilateral in the top row.
Outcomes
Rhombus
Square
Parallelogram
H, P
S, P
Rectangle
H, R
S, R
Square
H, S
S, S
Trapezoid
H, T
S, T
Rhombus
H, H
S, H
Tree Diagram
Let's now draw a tree diagram to represent the situation.
