Question
A deli sandwich shop is offering either a ham or turkey sandwich, either tomato or vegetable soup, and either coffee or milk for their lunch special. What is the probability that a customer will choose vegetable soup as part of the chosen combination?
Answers
GPT-4o mini
To determine the probability that a customer will choose vegetable soup as part of their lunch combination, we first need to understand the total combinations available for the lunch special.
1. **Sandwich Options**: There are 2 choices - ham or turkey.
2. **Soup Options**: There are 2 choices - tomato or vegetable.
3. **Drink Options**: There are 2 choices - coffee or milk.
Now, we can find the total number of unique combinations by multiplying the number of choices in each category:
\[
\text{Total combinations} = (\text{sandwich choices}) \times (\text{soup choices}) \times (\text{drink choices}) = 2 \times 2 \times 2 = 8.
\]
Next, we will determine how many of these combinations include vegetable soup.
- There are still 2 options for the sandwich (ham or turkey).
- There is only 1 option for the soup (vegetable).
- There are 2 options for the drink (coffee or milk).
So, the combinations that include vegetable soup are:
\[
\text{Vegetable Soup combinations} = (\text{sandwich choices}) \times (\text{soup choice}) \times (\text{drink choices}) = 2 \times 1 \times 2 = 4.
\]
Finally, we can find the probability that a customer will choose vegetable soup as part of their combination by taking the number of combinations that include vegetable soup and dividing it by the total number of combinations:
\[
\text{Probability (vegetable soup)} = \frac{\text{Vegetable Soup combinations}}{\text{Total combinations}} = \frac{4}{8} = \frac{1}{2}.
\]
Thus, the probability that a customer will choose vegetable soup as part of their chosen combination is \(\frac{1}{2}\).
1. **Sandwich Options**: There are 2 choices - ham or turkey.
2. **Soup Options**: There are 2 choices - tomato or vegetable.
3. **Drink Options**: There are 2 choices - coffee or milk.
Now, we can find the total number of unique combinations by multiplying the number of choices in each category:
\[
\text{Total combinations} = (\text{sandwich choices}) \times (\text{soup choices}) \times (\text{drink choices}) = 2 \times 2 \times 2 = 8.
\]
Next, we will determine how many of these combinations include vegetable soup.
- There are still 2 options for the sandwich (ham or turkey).
- There is only 1 option for the soup (vegetable).
- There are 2 options for the drink (coffee or milk).
So, the combinations that include vegetable soup are:
\[
\text{Vegetable Soup combinations} = (\text{sandwich choices}) \times (\text{soup choice}) \times (\text{drink choices}) = 2 \times 1 \times 2 = 4.
\]
Finally, we can find the probability that a customer will choose vegetable soup as part of their combination by taking the number of combinations that include vegetable soup and dividing it by the total number of combinations:
\[
\text{Probability (vegetable soup)} = \frac{\text{Vegetable Soup combinations}}{\text{Total combinations}} = \frac{4}{8} = \frac{1}{2}.
\]
Thus, the probability that a customer will choose vegetable soup as part of their chosen combination is \(\frac{1}{2}\).