A bag contains three balls numbered one to three. In an experiment, a ball is selected at random from the bag, replaced, and then another ball is selected. How many possible outcomes are there?
The first thing that happens is that someone draws a ball from the bag. The possible outcomes from the first draw are one, two, or three. No matter which number is drawn out the first time, it goes back into the bag and we draw again. If you drew one on draw one, your second draw could be one, two, or three.
If you drew two on draw one, your second drawer could be one, two, or three. The same is true if we drew the number three in the first round. In the second round, we could draw one, two, or three. This tree helps us visualize all the possible outcomes: one one, one two, one three, two one, two two, two three, three one, three two, or three three.
First round, three options. Second round, three options. Nine total possible outcomes.