To determine the probability of the complement of choosing an orange juice box from the cooler, let's follow a step-by-step procedure:
1. Count the Total Number of Juice Boxes:
- Apple juice boxes: 4
- Orange juice boxes: 8
- Fruit punch juice boxes: 6
Adding these together gives us the total number of juice boxes:
[tex]\[
4 + 8 + 6 = 18
\][/tex]
2. Calculate the Probability of Choosing an Orange Juice Box:
The probability of choosing an orange juice box is the ratio of the number of orange juice boxes to the total number of juice boxes:
[tex]\[
\frac{\text{Number of orange juice boxes}}{\text{Total number of juice boxes}} = \frac{8}{18} = \frac{4}{9}
\][/tex]
3. Determine the Complement of Choosing an Orange Juice Box:
The complement of an event is 1 minus the probability of the event occurring. Hence, the probability of not choosing an orange juice box is:
[tex]\[
1 - \left(\frac{4}{9}\right) = \frac{9}{9} - \frac{4}{9} = \frac{5}{9}
\][/tex]
Therefore, the probability of the complement of choosing an orange juice box is:
[tex]\[
\boxed{\frac{5}{9}}
\][/tex]
