the cooler at a picnic contained 4 apple juice boxes, 8 orange juice boxes, and 6 fruit punch juice boxes. a…

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?\n\\(\\frac{1}{18}\\)\n\\(\\frac{4}{9}\\)\n\\(\\frac{5}{9}\\)\n\\(\\frac{17}{18}\\)

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?\n\\(\\frac{1}{18}\\)\n\\(\\frac{4}{9}\\)\n\\(\\frac{5}{9}\\)\n\\(\\frac{17}{18}\\)

Answer

Explanation:

Step1: Calculate total juice - boxes

The total number of juice - boxes is the sum of apple, orange, and fruit - punch juice boxes. So, $4 + 8+6=18$ juice - boxes.

Step2: Calculate probability of choosing an orange juice box

The probability of choosing an orange juice box, $P(O)$, is the number of orange juice boxes divided by the total number of juice boxes. So, $P(O)=\frac{8}{18}=\frac{4}{9}$.

Step3: Calculate the probability of the complement

The probability of the complement of an event $A$, denoted as $P(A')$, is given by $P(A') = 1 - P(A)$. Here, the event $A$ is choosing an orange juice box. So, $P(O')=1 - P(O)=1-\frac{4}{9}=\frac{9 - 4}{9}=\frac{5}{9}$.

Answer:

$\frac{5}{9}$