Question

1. at a pizza shop, you can choose thick or thin crust, red or white sauce, and toppings of pepperoni, cheese, or vegetarian. create a tree diagram to display the sample space.

Explanation:

Step1: Identify first category

Crust options: Thick, Thin

Step2: Add second category branches

For each crust, add sauce options: Red, White

Step3: Add third category branches

For each sauce, add topping options: Pepperoni, Cheese, Vegetarian

Step4: Map all sample space outcomes

Combine each path of crust → sauce → topping

Answer:

Tree Diagram Structure:

Start
├─ Thick Crust
│  ├─ Red Sauce
│  │  ├─ Pepperoni
│  │  ├─ Cheese
│  │  └─ Vegetarian
│  └─ White Sauce
│     ├─ Pepperoni
│     ├─ Cheese
│     └─ Vegetarian
└─ Thin Crust
   ├─ Red Sauce
   │  ├─ Pepperoni
   │  ├─ Cheese
   │  └─ Vegetarian
   └─ White Sauce
      ├─ Pepperoni
      ├─ Cheese
      └─ Vegetarian

Full Sample Space:

1. Thick, Red, Pepperoni
2. Thick, Red, Cheese
3. Thick, Red, Vegetarian
4. Thick, White, Pepperoni
5. Thick, White, Cheese
6. Thick, White, Vegetarian
7. Thin, Red, Pepperoni
8. Thin, Red, Cheese
9. Thin, Red, Vegetarian
10. Thin, White, Pepperoni
11. Thin, White, Cheese
12. Thin, White, Vegetarian