Let's solve this problem step by step:
1. Identify the total number of possible outcomes:
- There are 3 options for an appetizer: Veggie plate, Salad, Soup.
- There are 3 options for an entrée: Steak, Chicken, Fish.
- There are 3 options for a drink: Water, Lemonade, Iced Tea.
To find the total number of possible combinations, we multiply the number of options for each category:
[tex]\[
3 \text{ (appetizers)} \times 3 \text{ (entrées)} \times 3 \text{ (drinks)} = 27
\][/tex]
So, the total number of possible outcomes is \( 27 \).
2. Identify the number of favorable outcomes:
- We are interested in the specific combination of Soup (appetizer), Chicken (entrée), and Iced Tea (drink).
- Since this is just one specific combination, there is only 1 favorable outcome.
So, the number of favorable outcomes is \( 1 \).
3. Calculate the probability:
- Probability is the ratio of the number of favorable outcomes to the total number of possible outcomes.
[tex]\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{1}{27} \approx 0.037037
\][/tex]
Putting it all together:
- Total number of possible outcomes = \( 27 \)
- Number of favorable outcomes = \( 1 \)
- Probability = \( \frac{1}{27} \approx 0.037037 \)
Hence, the probability that Brian chooses soup, chicken, and iced tea is approximately [tex]\( 0.037037 \)[/tex] or [tex]\( \frac{1}{27} \)[/tex].
