Exercise 45 Page 905

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 Lesson — drums or guitar
• Second Lesson — drums or guitar

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 choice of lessons in the first year are drums (D) or guitar (G). There are also two possible outcomes for the choice in the second year, drums (D) or guitar (G). We will pair each possible outcome from the first choice with the possible outcomes from the second choice. lcl D, D & & G, D D, G & & G, G

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.

Tree Diagram

Let's now draw a tree diagram to represent the situation.