Question

There are 28 balloons in a bag: 7 each of blue, green, red and yellow. Three balloons arechosen at random. Find the probability that all three balloons are green.Hint:combination greencombination total

Answer 1

Hello!

First, let's write the probability of each event:

Choose a green balloon:

`P(green)=\frac{\text{green balloons}}{\text{total of balloons}}`

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:

`P(green)=\frac{\text{7}}{28}=(1)/(4)=0.25`

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:

`P(1)=(7)/(28)=(1)/(4)`

Now, this green balloon was removed, so we have 27 balloons in the bag, of which 6 are green:

`P(2)=(6)/(27)=(2)/(9)`

Again, this balloon was removed too, remaining at this moment 26 balloons of which 5 are green:

`\begin{gathered} P(3)=(5)/(26) \\ \end{gathered}`

So, we have to multiply these three probabilities:

P(1) * P(2) * (P3):