Answer:
[tex]\dfrac{1}{14}[/tex].
Step-by-step explanation:
It is given that,
Red marbles = 3
Blue marbles = 7
Orange marbles = 5
Total marbles = 3+7+5 = 15
Probability of getting a red marble is
[tex]P(Red)=\dfrac{\text{Red marbles}}{\text{Total marbles}}[/tex]
[tex]P(Red)=\dfrac{3}{15}[/tex]
[tex]P(Red)=\dfrac{1}{5}[/tex]
If a marble is drawn from the bag and not replaced. So remaining marbles is 15-1=14. Now,
Probability of getting an orange marble is
[tex]P(orange )=\dfrac{\text{Orange marbles}}{\text{Total remaining marbles}}[/tex]
[tex]P(orange)=\dfrac{5}{14}[/tex]
Now,
[tex]P(\text{red then orange})=P(Red)\times P(orange)[/tex]
[tex]P(\text{red then orange})=\dfrac{1}{5}\times \dfrac{5}{14}[/tex]
[tex]P(\text{red then orange})=\dfrac{1}{14}[/tex]
Therefore, the required probability is [tex]\dfrac{1}{14}[/tex].
