Answer:
[tex]P(\text{Not blue})=\frac{3}{4}[/tex]
Step-by-step explanation:
We have been given that a bag contains 8 red marbles 3 blue marbles and 1 green marble. We are asked to find the probability of not getting a blue marble.
Probability of not getting a blue marble will be equal to probability of getting red marble plus probability of getting green marble.
[tex]P(Red)=\frac{8}{8+3+1}[/tex]
[tex]P(Red)=\frac{8}{12}[/tex]
[tex]P(Green)=\frac{1}{8+3+1}[/tex]
[tex]P(Green)=\frac{1}{12}[/tex]
[tex]P(\text{Not blue})=P(\text{Red})+P(\text{Green})[/tex]
[tex]P(\text{Not blue})=\frac{8}{12}+\frac{1}{12}[/tex]
[tex]P(\text{Not blue})=\frac{8+1}{12}[/tex]
[tex]P(\text{Not blue})=\frac{9}{12}[/tex]
[tex]P(\text{Not blue})=\frac{3*3}{3*4}[/tex]
[tex]P(\text{Not blue})=\frac{3}{4}[/tex]
Therefore, the probability of not getting a blue marble is [tex]\frac{3}{4}[/tex].
