We are given an experiment and want to find the total number of outcomes. We can do this by finding the sample space. Recall that the sample space an experiment is the set of all possible outcomes. In this case, the sample space is the result of two stages, picking a sporting goods store and then picking a school supplies store.
Sporting Goods Store — G1 or G2 or G3
School Supplies Store — S1 or S2 or S3 or S4
Let's now draw a tree diagram to represent the situation. First, we will consider choosing sporting goods store G1.
The graph tells us that there are 4 possible outcomes when first visiting store G1 and then one of the school supplies stores. Next, let's do the same for store G2.
As we can see, there are also 4 outcomes in this situation. Finally, let's check for store G3.
In this case, we also have 4 possible outcomes. The total number of possible outcomes is the sum of the elements in all sample spaces. This means there is a total of 12 possible outcomes in the situation from the exercise.
