At a museum cafe, you can get a pre-made boxed lunch with a sandwich, fruit, and drink for only [tex]$\$[/tex]3[tex]$.

- The sandwiches are made with either turkey or ham.
- The fruit is either an apple or an orange.
- The drink is either bottled water or juice.

The number of boxes they make for every possible combination is the same. If you randomly choose one of the boxed lunches without knowing the contents, what is the probability you will get a turkey sandwich and a bottle of water in your box?

A. $[/tex]\frac{1}{8}[tex]$
B. $[/tex]\frac{1}{2}[tex]$
C. $[/tex]\frac{1}{4}[tex]$
D. $[/tex]\frac{1}{3}$



Answer :

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].