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?

1/18
4/9
5/9
17/18

Answer 1

Answer:  The correct option is (C) $\dfrac{5}{9}.$

Step-by-step explanation:  Given that the cooler at a picnic contained 4 apple juice boxes, 8 orange juice boxes, and 6 fruit punch juice boxes.

We are to find the probability of the complement of choosing an orange juice box if one box is chosen at random.

Let "A", "B" an "C" be the events of choosing an apple juice box, an orange juice box and a fruit punch juice box.

Then, according to the given information, we have

n(A) = 4,  n(B) = 8  and n(C) = 6.

Therefore, the probability of choosing an orange juice box is given by

$P(B)=\dfrac{n(B)}{n(A)+n(B)+n(C)}=\dfrac{8}{4+8+6}=\dfrac{8}{18}=\dfrac{4}{9}.$

Thus, the probability of the complement of  choosing an orange juice box will be

$P(A')=1-P(A)=1-\dfrac{4}{9}=\dfrac{5}{9}.$

Hence, the correct option is (C) $\dfrac{5}{9}.$

Answer 2

Answer: $\dfrac{5}{9}$

Step-by-step explanation:

Given: Number of orange juice boxes = 8

Total number of juice boxes = $4+8+6=18$

Now if a juice box is selected at random, then the probability of the complement of choosing an orange juice box is given by :-

$\text{P(orange)}=\dfrac{8}{18}=\dfrac{4}{9}$

Now, the probability of the complement of choosing an orange juice box will be :-

$\text{P(orange)}'=1-\text{P(orange)}\\\\=1-\dfrac{4}{9}\\\\=\dfrac{5}{9}$

Hence, the probability of the complement of choosing an orange juice box =$\dfrac{5}{9}$