Question

texes mathematics 4-8 (115)
competency 13 (part 4): real-world applications

1. a restaurant has 2 different soups, 3 different main courses, and 5 different beverages with a meal deal consisting of one item from each category. suppose chicken soup is one of the soups and coffee is one of the beverages. if you order 1 soup and 1 beverage, what is the probability that your meal will have chicken soup and coffee?

Explanation:

⚡ Using what you learned: Simple Events and Compound Events

Step 1: Find the total number of possible meal combinations

Using the Fundamental Counting Principle, multiply the number of options in each category:

• Soups: \(2\)
• Main courses: \(3\)
• Beverages: \(5\)

$$ \text{Total combinations} = 2 \times 3 \times 5 = 30 $$

Step 2: Find the number of favorable outcomes

We want to find the number of combinations that include:

• Chicken soup (exactly \(1\) specific soup option)
• Any main course (\(3\) options)
• Coffee (exactly \(1\) specific beverage option)

$$ \text{Favorable combinations} = 1 \times 3 \times 1 = 3 $$

Step 3: Calculate the probability

Divide the number of favorable outcomes by the total number of outcomes:

$$ P(\text{chicken soup, any main, coffee}) = \frac{3}{30} = \frac{1}{10} $$

Answer:

\(\frac{1}{10}\) (or \(0.1\), which is \(10\%\))