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?\no $\frac{1}{18}$\no $\frac{4}{9}$\no $\frac{5}{9}$\no $\frac{17}{18}$

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?\no $\frac{1}{18}$\no $\frac{4}{9}$\no $\frac{5}{9}$\no $\frac{17}{18}$

Answer

Explanation:

Step1: Calculate total number of juice - boxes

$4 + 8+6=18$

Step2: Calculate probability of choosing an orange juice box

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

Step3: Calculate the probability of the complement

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

Answer:

$\frac{5}{9}$