Question

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

• 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?
1/3
1/2
1/8
1/4

Explanation:

Step1: Calculate total number of combinations

Use the counting principle. Number of sandwich choices \(n_1 = 2\) (turkey or ham), number of fruit choices \(n_2=2\) (apple or orange), number of drink choices \(n_3 = 2\) (bottled water or juice). Total number of combinations \(N=n_1\times n_2\times n_3\).

$$N = 2\times2\times2=8$$

Step2: Calculate probability

Probability \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). There is \(1\) favorable outcome (turkey - apple - bottled water).

$$P=\frac{1}{8}$$

Answer:

\(\frac{1}{8}\) (corresponds to the third option)