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?

Explanation:

Step1: Calculate the total number of juice boxes

The total number of juice boxes is \(4 + 8+6=18\).

Step2: Find the probability of choosing an orange juice box

The probability of choosing an orange juice box \(P(\text{orange})\) is \(\frac{8}{18}=\frac{4}{9}\) (using the formula \(P=\frac{\text{number of favorable outcomes}}{\text{total number of outcomes}}\)).

Step3: Use the complement rule

The complement rule states that \(P(\text{complement of }A)=1 - P(A)\). Let \(A\) be the event of choosing an orange juice box. Then \(P(\text{complement of choosing an orange juice box})=1-\frac{4}{9}=\frac{9 - 4}{9}=\frac{5}{9}\)

Answer:

\(\frac{5}{9}\)