Respuesta :
Explanation
We are asked to resolve a conditional probability question
For the given question, we will have to find the probability of obtaining a green marble given not yellow
We have the box containing one green marble, two yellow marbles, and six pink marbles
Green = 1
Yellow = 2
Pink = 6
Probability is the ratio of the number of possible outcomes to the total outcomes
we will apply the formula
[tex]P(G|Y^{\prime})=\frac{P(G\text{ n Y'})}{P(Y^{\prime})}[/tex]Where
[tex]P(G)=probability\text{ of green marble=G=}\frac{1}{9}[/tex][tex]\begin{gathered} P(Y)=probability\text{ of Yellow = }\frac{2}{9} \\ \\ P(Y^{\prime})=probab\imaginaryI l\imaginaryI ty\text{ of not Yellow=1-}\frac{2}{9}=\frac{7}{9} \end{gathered}[/tex]Thus
[tex]\begin{gathered} P(G\text{ n }Y^{\prime})=\frac{1}{9} \\ \\ P(Y^{\prime})=\frac{7}{9} \end{gathered}[/tex]Therefore, we will have the answer as
[tex]P(G|Y^{\prime})=\frac{1}{9}\div\frac{7}{9}=\frac{1}{9}\times\frac{9}{7}=\frac{1}{7}[/tex]Therefore, the answer will be
[tex]\frac{1}{7}[/tex]