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\begin{tabular}{|c|}
\hline
Dinner Menu \\
\hline
Appetizers: \\
Veggie plate, salad, soup \\
\hline
Entrées: \\
Steak, chicken, fish \\
\hline
Drinks: \\
Water, lemonade, iced tea \\
\hline
\end{tabular}

Brian is choosing an appetizer, an entrée, and a drink. If he chooses an item from each list at random, what is the probability that he chooses soup, chicken, and iced tea?

Total number of possible outcomes [tex]$= 27$[/tex]

Number of favorable outcomes [tex]$= 1$[/tex]

Probability [tex]$= \frac{1}{27}$[/tex]



Answer :

GinnyAnswer
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].

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