Let A, O and F be the events of choosing Apple juice, Orange Juice and Fruit punch. Then we have,
[tex]\begin{gathered} n(A)=4 \\ n(O)=8 \\ n(F)=6 \end{gathered}[/tex]
Therefore, the probability of choosing the orange juice is,
[tex]P(O)=\frac{n(O)}{n(A)+n(O)+n(F)}=\frac{8}{4+8+6}=\frac{8}{18}=\frac{4}{9}[/tex]
Now, the probbaility of complement of choosing the orange juice box is,
[tex]\begin{gathered} P(O)+P^{\prime}(O)=1 \\ P^{\prime}\text{(O)=}1-P(O)_{} \\ P^{\prime}(O)=1-\frac{4}{9}=\frac{9-4}{9}=\frac{5}{9} \end{gathered}[/tex]
Thus, the third option is correct.
