Question

Josie bought two packages of balloons. Each package contains four red balloons, four green balloons, and four blue balloon balloons. What is the probability that Josie will randomly select one red balloon from both bags
1/3
1/16
1/12
1/9

Answer 1

First, let's analyze the contents of the two packages of balloons. Each package contains:

- 4 red balloons
- 4 green balloons
- 4 blue balloons

Therefore, the total number of balloons in one package is:

\[ 4 \text{ (red)} + 4 \text{ (green)} + 4 \text{ (blue)} = 12 \text{ balloons} \]

Since Josie bought two packages, the total number of balloons she has is:

\[ 2 \times 12 = 24 \text{ balloons} \]

Among these 24 balloons, the total number of red balloons is:

\[ 2 \times 4 = 8 \text{ red balloons} \]

Now, we want to find the probability that Josie selects one red balloon from each bag.

When selecting one balloon from each package, the number of ways to select a red balloon from the first package is:

\[ \frac{4 \text{ (red balloons in Package 1)}}{12 \text{ (total balloons in Package 1)}} = \frac{4}{12} = \frac{1}{3} \]

For the second package, the probability of selecting a red balloon is the same:

\[ \frac{4 \text{ (red balloons in Package 2)}}{12 \text{ (total balloons in Package 2)}} = \frac{4}{12} = \frac{1}{3} \]

Since the selections are independent, the probability of selecting a red balloon from both packages is:

\[
\text{P(Red from Package 1 and Red from Package 2)} = P(Red from Package 1) \times P(Red from Package 2) = \frac{1}{3} \times \frac{1}{3} = \frac{1}{9}
\]

Therefore, the probability that Josie will randomly select one red balloon from both bags is \(\frac{1}{9}\).

So the answer is:

\(\frac{1}{9}\)