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 an orange and not get juice in your box?
○ 1/8
○ 1/2
○ 1/3
○ 1/4

Explanation:

Step1: Calculate total combinations

Use the counting principle. There are \(2\) (sandwich options) \(\times2\) (fruit options) \(\times2\) (drink options) \(= 2\times2\times2=8\) total combinations.

Step2: Find favorable combinations

We want orange (1 fruit option) and not - juice (i.e., bottled water, 1 drink option). The sandwich can be either turkey or ham (2 options). So the number of favorable combinations is \(2\times1\times1 = 2\).

Step3: Calculate probability

Probability \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). So \(P=\frac{2}{8}=\frac{1}{4}\)

Answer:

\(\frac{1}{4}\)