Scenario: You are going to have 2 pets (they're easier than kids). You are equally likely to select a cat, dog, fish, or hamster each time you choose a new pet. Assume the order matters. In other words, choosing a dog then a cat is not the same as choosing a cat then a dog, just like having a boy then a girl was not the same as having a girl then a boy.

Part 1

1. Use a tree diagram to come up with the sample space.

2. Create a probability distribution for each outcome (E) in your sample space. (This is a table that would show each outcome DC or CD, etc, and the probability of each of those outcomes.)

3. Draw a graph of that distribution. Be sure to label your x and y axis appropriately.

Part 2

1. Create another frequency distribution (table) based on the number of dogs you might end up with. X is now quantitative and represents the number of dogs.

2. Draw a graph of this distribution.

Questions:

1. How many outcomes are in the sample space n(S)?

2. In your frequency distribution for Part 1, what is the probability for each event?

3. In your graph of the frequency distribution for Part 2, what is the most appropriate label and data to put along the x axis?

4. In your frequency distribution for Part 2, what is the probability that you have no dogs? That is, what is P(X = 0)?

5. In your frequency distribution for Part 2, what is the probability that you have 1 dog? That is, what is P(X = 1)?

6. In your frequency distribution for Part 2, what is the probability that you have two dogs? That is, what is P(X = 2)?

7. In your frequency distribution for Part 2, what is the probability that you have 3 dogs? That is, what is P(X = 3)?

8. What is the shape of your graph for the frequency distribution in part 2?