At a museum cafe you can get a pre-made boxed lunch with a sandwich, fruit, and drink for only $3

Question

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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?

Answer 1

To determine the probability of getting a boxed lunch with a turkey sandwich, an apple, and a bottle of water, we need to first calculate the total number of possible combinations of the boxed lunch.

1. Choices for Sandwich: There are 2 options (turkey or ham).
2. Choices for Fruit: There are 2 options (apple or orange).
3. Choices for Drink: There are 2 options (bottled water or juice).

Now, we can calculate the total number of combinations by multiplying the number of choices for each category:

\[ \text{Total combinations} = (\text{Choices for Sandwich}) \times (\text{Choices for Fruit}) \times (\text{Choices for Drink}) = 2 \times 2 \times 2 = 8 \]

Next, we want to find the specific combination we are interested in:

• Turkey sandwich
• Apple
• Bottled water

There is only 1 specific combination that meets these criteria.

Finally, we can calculate the probability of randomly selecting this combination:

\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total combinations}} = \frac{1}{8} \]

Thus, the probability of getting a turkey sandwich, an apple, and a bottle of water in your box is \(\frac{1}{8}\).