Question

A caterer makes 74 Jamaican patties with 3 different types of filling and 2 levels of spiciness. The table shows the number of each type of patty. Let X be the event that a patty chosen at random has beef or chicken and is spicy.
Lola says that there are 10 outcomes in the complement of X. Is Lola correct? Use the drop-down menus to explain.

Spicy
Mild
Beef
12
15
Chicken
12
15
Vegetarian
10
10
Jamaican PattiesClick the arrows to choose an answer from each menu.
The number of outcomes in X is
Choose..
Choose...
"
. Lola is
Choose...
• . The number of outcomes in the complement

Answer 1

To determine whether Lola is correct, let's first analyze the table of Jamaican patties.

**Given Data:**
- **Spicy Beef Patties**: 12
- **Mild Beef Patties**: 15
- **Spicy Chicken Patties**: 12
- **Mild Chicken Patties**: 15
- **Spicy Vegetarian Patties**: 10
- **Mild Vegetarian Patties**: 10

First, we find the total number of outcomes for each type of patty:
- Beef: 12 (spicy) + 15 (mild) = 27
- Chicken: 12 (spicy) + 15 (mild) = 27
- Vegetarian: 10 (spicy) + 10 (mild) = 20

**Total Number of Patties**: 74, which matches the provided data.

Now, we define the event **X**:
- Event X is that a patty has beef or chicken and is spicy.
- This means we include only spicy beef and spicy chicken patties.

Calculating the number of outcomes in event X:
- Spicy Beef: 12
- Spicy Chicken: 12

**Number of outcomes in X**: \( 12 + 12 = 24 \)

Next, we find the complement of event X, which includes all other patties (mild beef, mild chicken, spicy vegetarian, mild vegetarian):
- Mild Beef: 15
- Mild Chicken: 15
- Spicy Vegetarian: 10
- Mild Vegetarian: 10

Calculating the number of outcomes in the complement of X:
- Mild Beef: 15
- Mild Chicken: 15
- Spicy Vegetarian: 10
- Mild Vegetarian: 10

**Number of outcomes in the complement of X**:
\( 15 + 15 + 10 + 10 = 50 \)

Now, let's address Lola's claim that there are 10 outcomes in the complement of X.

**Answering Lola's claim**:
- The number of outcomes in X is **24**.
- The number of outcomes in the complement of X is **50**.
- Therefore, Lola is **not correct**.

If you would like to fill in the blanks using the drop-down menus, you can use:
1. The number of outcomes in X is **24**.
2. Lola is **not correct**.
3. The number of outcomes in the complement is **50**.