Let's break down the problem step by step.
1. Identify the choices for each category in the boxed lunch:
- Sandwich options: There are two choices, turkey and ham.
- Fruit options: There are two choices, apple and orange.
- Drink options: There are two choices, bottled water and juice.
2. Calculate the total number of possible combinations:
To find the total number of different boxed lunches possible, we multiply the number of choices for each category together:
[tex]\[
\text{Total combinations} = (\text{Number of sandwich options}) \times (\text{Number of fruit options}) \times (\text{Number of drink options})
\][/tex]
Substituting the values, we get:
[tex]\[
\text{Total combinations} = 2 \times 2 \times 2 = 8
\][/tex]
This means there are 8 different possible combinations of boxed lunches.
3. Determine the number of favorable outcomes:
We are interested in the boxed lunch that includes a turkey sandwich and bottled water. Let's see how many such combinations are possible:
- For the sandwich: turkey (1 option)
- For the fruit: it can either be apple or orange (2 options)
- For the drink: bottled water (1 option)
So, there are:
[tex]\[
\text{Number of favorable outcomes} = 1 (\text{turkey}) \times 2 (\text{fruit}) \times 1 (\text{bottled water}) = 1
\][/tex]
4. Calculate the probability:
The probability of an event is given by:
[tex]\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}
\][/tex]
Plugging in the values:
[tex]\[
\text{Probability} = \frac{1}{8}
\][/tex]
Therefore, the probability that you will get a boxed lunch with a turkey sandwich and bottled water is:
[tex]\[
\boxed{\frac{1}{8}}
\][/tex]
