Question

What is the probability of the complement of choosing an orange juice box?

Answer 1

Let A, O and F be the events of choosing Apple juice, Orange Juice and Fruit punch. Then we have,

`\begin{gathered} n(A)=4 \\ n(O)=8 \\ n(F)=6 \end{gathered}`

Therefore, the probability of choosing the orange juice is,

`P(O)=(n(O))/(n(A)+n(O)+n(F))=(8)/(4+8+6)=(8)/(18)=(4)/(9)`

Now, the probbaility of complement of choosing the orange juice box is,

`\begin{gathered} P(O)+P^(\prime)(O)=1 \\ P^(\prime)\text{(O)=}1-P(O)_{} \\ P^(\prime)(O)=1-(4)/(9)=(9-4)/(9)=(5)/(9) \end{gathered}`

Thus, the third option is correct.