Hello!
First, let's write the probability of each event:
Choose a green balloon:
[tex]P(green)=\frac{\text{green balloons}}{\text{total of balloons}}[/tex]Let's find the probability of the first balloon be green:
We have 28 balloons in the bag, and we have to pick one green at random. At this moment, we have 7 green balloons. So, let's use the formula above:
[tex]P(green)=\frac{\text{7}}{28}=\frac{1}{4}=0.25[/tex]If we consider that after the draw the balloon was returned to the bag:
As we already know that the probability of choosing one green balloon is 1/4, now we have to find the probability of three green balloons, look:
So, the probability of choosing 3 green balloons with replacement is 1/64.
Now, I'll solve considering that after the drawn the balloons were removed:
For the first drawn, we have 28 balloons in the bag, of which 7 are green. So, we have:
[tex]P(1)=\frac{7}{28}=\frac{1}{4}[/tex]Now, this green balloon was removed, so we have 27 balloons in the bag, of which 6 are green:
[tex]P(2)=\frac{6}{27}=\frac{2}{9}[/tex]Again, this balloon was removed too, remaining at this moment 26 balloons of which 5 are green:
[tex]\begin{gathered} P(3)=\frac{5}{26} \\ \end{gathered}[/tex]So, we have to multiply these three probabilities:
P(1) * P(2) * (P3):
