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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?

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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
  1. 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.