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, an apple, and a bottle of water in your box?

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



Answer :

To solve this problem, we first need to understand the different combinations that can be made from the available choices for sandwiches, fruits, and drinks.

### Step 1: Calculate the Total Number of Combinations

1. Sandwich choices: There are 2 options - turkey or ham.
2. Fruit choices: There are 2 options - apple or orange.
3. Drink choices: There are 2 options - bottled water or juice.

To find the total number of possible combinations, we multiply the number of choices for each category:

[tex]\[ 2 \text{ (sandwiches)} \times 2 \text{ (fruits)} \times 2 \text{ (drinks)} = 8 \text{ total combinations} \][/tex]

### Step 2: Identify the Desired Combination

The specific combination we are interested in is a turkey sandwich, an apple, and bottled water. This is just one unique combination out of the total combinations.

### Step 3: Calculate the Probability

The probability of selecting any specific combination out of the total possible combinations is given by:

[tex]\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \][/tex]

Here, there is only 1 favorable outcome (the combination of turkey sandwich, apple, and bottled water) out of a total of 8 possible combinations. So, the probability is:

[tex]\[ \text{Probability} = \frac{1}{8} \][/tex]

Therefore, if you randomly choose one of the boxed lunches without knowing the contents, the probability that you will get a turkey sandwich, an apple, and bottled water in your box is [tex]\(\frac{1}{8}\)[/tex].

Thus, the correct answer is:

[tex]\[ \boxed{\frac{1}{8}} \][/tex]