At a certain pizzeria, `(1)/(6)` of the pizzas sold in a week were cheese, and `(1)/(5)` of the OTHER pizzas sold were pepperoni. If Brandon bought a randomly chosen pizza from the pizzeria that week, what is the probability that he ordered a pepperoni?

Answer

To solve the problem, we need to find the probability that Brandon ordered a pepperoni pizza from the pizzeria. Let's break it down step by step.

### Step 1: Define the total number of pizzas
Let the total number of pizzas sold in a week be represented as \( N \).

### Step 2: Calculate the number of cheese pizzas
According to the problem, \( \frac{1}{6} \) of the pizzas sold were cheese. Therefore, the number of cheese pizzas can be calculated as:
\[ \text{Number of cheese pizzas} = \frac{1}{6} N \]

### Step 3: Calculate the number of other pizzas
The remaining pizzas (other than cheese) would be:
\[ \text{Number of other pizzas} = N - \frac{1}{6} N = \frac{5}{6} N \]

### Step 4: Calculate the number of pepperoni pizzas
We know that \( \frac{1}{5} \) of the other pizzas were pepperoni. Therefore, the number of pepperoni pizzas can be calculated as:
\[ \text{Number of pepperoni pizzas} = \frac{1}{5} \left(\frac{5}{6} N\right) = \frac{1}{6} N \]

### Step 5: Total number of pizzas
Now we can summarize the total number of pizzas:
- Cheese pizzas: \( \frac{1}{6} N \)
- Pepperoni pizzas: \( \frac{1}{6} N \)
- Other pizzas: \( \frac{5}{6} N - \frac{1}{6} N = \frac{4}{6} N \)

### Step 6: Calculate the probability of ordering a pepperoni pizza
The probability \( P \) of Brandon ordering a pepperoni pizza is given by the formula:
\[ P(\text{pepperoni}) = \frac{\text{Number of pepperoni pizzas}}{\text{Total number of pizzas}} = \frac{\frac{1}{6} N}{N} = \frac{1}{6} \]

### Final Answer
Thus, the probability that Brandon ordered a pepperoni pizza is:
\[ \frac{1}{6} \]

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