To solve this problem, consider all possible combinations of the items in a boxed lunch.
1. Determine the total number of possible combinations:
- There are 2 choices for the sandwich (turkey, ham).
- There are 2 choices for the fruit (apple, orange).
- There are 2 choices for the drink (bottled water, juice).
To find the total number of combinations, you multiply the number of choices for each item:
[tex]\[
\text{Total combinations} = 2 \text{ (sandwich)} \times 2 \text{ (fruit)} \times 2 \text{ (drink)} = 8
\][/tex]
So there are 8 possible combinations for the boxed lunches.
2. Determine the number of favorable combinations:
- We need to find the probability of getting a boxed lunch with a turkey sandwich and bottled water.
- The turkey sandwich can be paired with either apple or orange, which gives us 2 possibilities.
- The drink must be bottled water, so there is only 1 choice for the drink for each fruit choice.
Thus, the favorable combinations are:
[tex]\[
2 \text{ (fruits)} \times 1 \text{ (bottled water)} = 2
\][/tex]
So, there are 2 favorable combinations (turkey sandwich with either apple or orange, both including bottled water).
3. Calculate the probability:
- The probability is the ratio of the number of favorable combinations to the total number of combinations.
[tex]\[
\text{Probability} = \frac{\text{Number of favorable combinations}}{\text{Total number of combinations}} = \frac{2}{8} = \frac{1}{4}
\][/tex]
Thus, the probability that you will get a turkey sandwich and a bottle of water in your boxed lunch is [tex]\(\frac{1}{4}\)[/tex].
The correct answer is [tex]\(\frac{1}{4}\)[/tex].
