You're ordering pizza from your favorite pizzeria, and they offer three different sizes (small, medium, large) and four different toppings (cheese, pepperoni, sausage, vegetarian). You want to know the probability of getting Medium with Pepperoni on top. Use the step-by-step process of creating a tree diagram and calculate possible probabilities.

To solve the problem of determining the probability of getting a medium pizza with pepperoni, let's break it down step-by-step using a tree diagram approach.

### Step 1: Understand the Possible Options
You are given the following:
- **Pizza Sizes**: Small, Medium, Large (3 options)
- **Toppings**: Cheese, Pepperoni, Sausage, Vegetarian (4 options)

### Step 2: Create a Tree Diagram

#### First Branch: Pizza Sizes
The first decision is choosing a pizza size. You have 3 options:
- Small
- Medium
- Large

#### Second Branch: Toppings
After selecting a pizza size, you then choose a topping. You have 4 options for toppings:
- Cheese
- Pepperoni
- Sausage
- Vegetarian

### Step 3: Calculate the Total Number of Outcomes
To get the total number of possible outcomes, multiply the number of choices for sizes by the number of choices for toppings:
\[
\text{Total Outcomes} = \text{Number of Sizes} \times \text{Number of Toppings} = 3 \times 4 = 12
\]

So, there are 12 possible outcomes when choosing both a size and a topping.

### Step 4: Identify the Desired Outcome
You want the probability of getting a **medium pizza with pepperoni**. There is only **1 specific outcome** that corresponds to this choice.

### Step 5: Calculate the Probability
The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In this case, the number of favorable outcomes is 1 (medium pizza with pepperoni), and the total number of outcomes is 12.

Thus, the probability is:
\[
\text{Probability of Medium with Pepperoni} = \frac{1}{12}
\]

### Conclusion:
The probability of getting a medium pizza with pepperoni is \( \frac{1}{12} \).

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Would you like more details or have any further questions?

### Related Questions:
1. What is the probability of getting a large pizza with sausage?
2. How many outcomes include a vegetarian topping regardless of size?
3. What is the probability of getting any pizza with cheese?
4. How does the probability change if they add a fourth size (extra-large)?
5. If you only like medium pizzas, what's the probability of getting one of your favorite toppings?

### Tip:
Tree diagrams are a great way to visualize sequential choices and can simplify probability calculations!

Learn how to calculate the probability of getting a medium pizza with pepperoni using a tree diagram approach. This problem covers probability concepts, including combinatorics and the basic probability theorem, and provides a step-by-step breakdown. Suitable for students in Grades 6-8.

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