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]
### 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]
