Example Organized List:
lcl
O, I & & A, I
O, S & & A, S
Example Table:
Outcomes
Isosceles Triangle
Scalene Triangle
Obtuse Triangle
O, I
O, S
Acute Triangle
A, I
A, S
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.
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 first exercise of the exam are an obtuse triangle (O) or an acute triangle (A). There are also two possible outcomes for the second exercise, an isosceles triangle (I) or a scalene triangle (S). We will pair each possible outcome from the first exercise with the possible outcomes from the second exercise.
lcl
O, I & & A, I
O, S & & A, S
Table
To make the table, we will list the outcomes of the first exercise in the left column and the outcomes of the second exercise in the top row.
Outcomes
Isosceles Triangle
Scalene Triangle
Obtuse Triangle
O, I
O, S
Acute Triangle
A, I
A, S
Tree Diagram
Let's now draw a tree diagram to represent the situation.
