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 find the probability of getting a medium pizza with pepperoni topping, we can use a step-by-step approach of creating a tree diagram and calculating the probabilities.

### Step-by-Step Process:

#### Step 1: List the possible outcomes for pizza size.
- There are **3 different sizes**: Small, Medium, Large.

This gives us three branches for the size selection:
- Small
- Medium
- Large

#### Step 2: List the possible outcomes for toppings.
- There are **4 different toppings**: Cheese, Pepperoni, Sausage, Vegetarian.

For each size (Small, Medium, Large), there will be four branches for the topping selection:
- Cheese
- Pepperoni
- Sausage
- Vegetarian

#### Step 3: Construct the tree diagram.
1. First level: Choose a pizza size.
   - There are 3 branches for each size: Small, Medium, Large.
   
2. Second level: After choosing a size, choose a topping.
   - For each size branch, there are 4 branches for toppings: Cheese, Pepperoni, Sausage, Vegetarian.

This gives us a total of \( 3 \times 4 = 12 \) different combinations of size and topping.

Here’s a summary of the combinations:
- Small: Cheese, Pepperoni, Sausage, Vegetarian
- Medium: Cheese, Pepperoni, Sausage, Vegetarian
- Large: Cheese, Pepperoni, Sausage, Vegetarian

#### Step 4: Determine the desired outcome.
- We are interested in the combination of **Medium** and **Pepperoni**.

#### Step 5: Calculate the probability.
- Total number of possible outcomes: \( 12 \) (since there are 3 sizes and 4 toppings).
- The specific outcome we want (Medium with Pepperoni) is just **1** outcome.

Thus, the probability \( P \) of getting Medium with Pepperoni is:

\[
P(\text{Medium with Pepperoni}) = \frac{1}{12}
\]

### Final Answer:
The probability of getting a medium pizza with pepperoni is \( \frac{1}{12} \), or approximately **0.0833** (8.33%).

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Would you like to explore more details or ask any questions about this process? Here are 5 related questions to expand on the topic:

1. What is the probability of getting a large pizza with sausage topping?
2. How would the probability change if another topping (e.g., mushrooms) is added to the menu?
3. What is the probability of getting any pizza with vegetarian topping?
4. Can we calculate the probability of getting either a small or a large pizza with any topping?
5. How does adding an additional size option (e.g., Extra Large) impact the probabilities?

**Tip**: When calculating probabilities, always consider both the total possible outcomes and the specific favorable outcome.

Learn how to calculate the probability of getting a medium pizza with pepperoni topping using a tree diagram. This problem demonstrates key probability concepts, including event outcomes and total possibilities. Suitable for students in Grades 5-7.

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