Tree Diagrams

1. Tree Diagrams A tree diagramhelps us to identify and count all of the possible outcomes of an event by using branching.

2. Fruit Smoothie Smoothie sizes: Small, Medium, and Large Smoothie flavors: Strawberry, Banana, and Orange. How many different smoothies are available?

3. If your smoothie is selected randomly, what is the probability that you select a small smoothie? If your smoothie is selected randomly, what is the probability that you select a small, orange smoothie? If your smoothie is selected randomly, what is the probability that you select an orange smoothie?

4. Example #2 You will be attending two sessions at a science camp. At each session, you will be assigned to one of the following groups: red (R), green (G), blue (B), or yellow (Y). You will not be assigned to the same group for both sessions. Make a tree diagram to find all of the possible group assignments. (sample space)

5. If groups are selected randomly, what is the probability that your first group will be blue? If groups are selected randomly, what is the probability that your second group will be red? If groups are selected randomly, what is the probability that your first group will be blue, and your second group will be red?

6. Example #3 Find the probability of getting at least 2 heads when tossing a coin 3 times. (Hint: First make a tree diagram to find all the possible outcomes from flipping a coin three times.)

7. On Your Own You have a plum, a banana, an apple, an orange, and a pear. If you eat one now with lunch and eat one later for a snack, what are all the possible pairs of fruit you can select for lunch and the snack?

8. One more You have 6 movies. You want to watch one now, and a different one later. How many ways can you choose two movies to watch?