The Roberts family is shopping for a new vehicle. They are considering a minivan or an SUV. Each vehicle has three models; standard, sport, or luxury. The family has decided that they want a red vehicle. Explain how to make a tree diagram to show their options. How many choices do they have?

To create a tree diagram for the Roberts family's vehicle options, we need to break down the choices available into categories and then visualize them. Here’s how to do it step-by-step:

1. **Identify the Categories**:
- **Type of Vehicle**: There are two options – Minivan and SUV.
- **Model of Vehicle**: Each type (minivan or SUV) has three models – Standard, Sport, and Luxury.
- **Color**: The family is looking for a red vehicle, so all options will be filtered to include only red vehicles.

2. **Start with the Main Choice**:
- At the top of the tree, create a branch for "Type of Vehicle". Create two branches coming from this point: one for "Minivan" and one for "SUV".

3. **Add the Sub-Choices**:
- From each of those branches (Minivan and SUV), create three additional branches for the models: "Standard", "Sport", and "Luxury".

4. **Visual Representation**:
- The tree diagram can be represented as follows:

```
Vehicle Choices
/ \
Minivan SUV
/ | \ / | \
Standard Sport Luxury Standard Sport Luxury
```

5. **Count the Options**:
- For each vehicle type (Minivan and SUV), there are three models. Therefore, the total number of choices can be calculated as follows:
- For Minivan: 3 choices (Standard, Sport, Luxury)
- For SUV: 3 choices (Standard, Sport, Luxury)
- Total Choices = 3 (minivan options) + 3 (SUV options) = 6 choices.

Therefore, the Roberts family has a total of **6 choices** for red vehicles, which are:
1. Red Minivan - Standard
2. Red Minivan - Sport
3. Red Minivan - Luxury
4. Red SUV - Standard
5. Red SUV - Sport
6. Red SUV - Luxury

In summary, the tree diagram helps visualize their options, and the total choices available to them are 6.