Example Organized List:
lcl
S, S & & O, O
S, O & & O, S
Example Table:
Outcomes
Safe
Out
Safe
S, S
S, O
Out
O, S
O, O
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 Bat — Safe or Out
Second Bat — Safe or Out
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 bat are a safe (S) or an out (O). There are also two possible outcomes for the second bat, a safe (S) or an out (O). We will pair each possible outcome from the first bat with the possible outcomes from the second bat.
lcl
S, S & & O, O
S, O & & O, S
Table
To make the table, we will list the outcomes of the first bat in the left column and the outcomes of the second bat in the top row.
Outcomes
Safe
Out
Safe
S, S
S, O
Out
O, S
O, O
Tree Diagram
Let's now draw a tree diagram to represent the situation.
