Answer :
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]
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]