Question

The cooler at a picnic contained 4 apple juice boxes, 8 orange juice boxes, and 6 fruit punch juice boxes. A juice box is selected at random. What is the probability of the complement of choosing an orange juice box?
StartFraction 1 over 18 EndFraction
StartFraction 4 over 9 EndFraction
StartFraction 5 over 9 EndFraction
StartFraction 17 over 18 EndFraction

Answer 1

To find the probability of the complement of choosing an orange juice box, we first need to determine the total number of juice boxes and the number of juice boxes that are not orange.

1. **Total number of juice boxes:**
- Apple juice boxes: 4
- Orange juice boxes: 8
- Fruit punch juice boxes: 6

Total = 4 + 8 + 6 = 18 juice boxes

2. **Number of juice boxes that are not orange juice boxes:**
- Total juice boxes: 18
- Orange juice boxes: 8

Juice boxes that are not orange = 18 - 8 = 10

3. **Probability of selecting a juice box that is not orange:**
\[
P(\text{not orange}) = \frac{\text{Number of juice boxes not orange}}{\text{Total number of juice boxes}} = \frac{10}{18} = \frac{5}{9}
\]

Thus, the probability of the complement of choosing an orange juice box is:

\[
\frac{5}{9}
\]

Therefore, the answer is \(\frac{5}{9}\).