Question
Josie bought two packages of balloons. Each package contains 4 red balloons, 4 green balloons, and 4 blue balloons. What is the probability that Josie will randomly select 1 red balloon from both bags?(1 point)
Answers
GPT-4o mini
To find the probability that Josie will randomly select 1 red balloon from both packages, let's first determine the total number of balloons in each package.
Each package contains:
- 4 red balloons
- 4 green balloons
- 4 blue balloons
This means each package has a total of:
\[ 4 \, (\text{red}) + 4 \, (\text{green}) + 4 \, (\text{blue}) = 12 \, \text{balloons} \]
Since Josie bought two packages, the total number of red balloons is:
\[ 2 \, \text{packages} \times 4 \, (\text{red}) = 8 \, \text{red balloons} \]
And the total number of balloons:
\[ 2 \, \text{packages} \times 12 \, (\text{total per package}) = 24 \, \text{balloons} \]
Now, if Josie is to select 1 red balloon from both packages, we need to consider the selection process. Assuming that she picks one balloon from each package, we will calculate the probability of picking one red balloon from each package.
1. **Probability of selecting a red balloon from the first package:**
\[
P(\text{red from package 1}) = \frac{4 \, (\text{red balloons})}{12 \, (\text{total balloons})} = \frac{4}{12} = \frac{1}{3}
\]
2. **Probability of selecting a red balloon from the second package:**
\[
P(\text{red from package 2}) = \frac{4 \, (\text{red balloons})}{12 \, (\text{total balloons})} = \frac{4}{12} = \frac{1}{3}
\]
Since the selections from each package are independent events, the joint probability of both events occurring (selecting a red balloon from the first package and a red balloon from the second package) is calculated by multiplying the probabilities:
\[
P(\text{red from package 1 and red from package 2}) = P(\text{red from package 1}) \times P(\text{red from package 2}) = \frac{1}{3} \times \frac{1}{3} = \frac{1}{9}
\]
Thus, the probability that Josie will randomly select 1 red balloon from both bags is \( \frac{1}{9} \).
Each package contains:
- 4 red balloons
- 4 green balloons
- 4 blue balloons
This means each package has a total of:
\[ 4 \, (\text{red}) + 4 \, (\text{green}) + 4 \, (\text{blue}) = 12 \, \text{balloons} \]
Since Josie bought two packages, the total number of red balloons is:
\[ 2 \, \text{packages} \times 4 \, (\text{red}) = 8 \, \text{red balloons} \]
And the total number of balloons:
\[ 2 \, \text{packages} \times 12 \, (\text{total per package}) = 24 \, \text{balloons} \]
Now, if Josie is to select 1 red balloon from both packages, we need to consider the selection process. Assuming that she picks one balloon from each package, we will calculate the probability of picking one red balloon from each package.
1. **Probability of selecting a red balloon from the first package:**
\[
P(\text{red from package 1}) = \frac{4 \, (\text{red balloons})}{12 \, (\text{total balloons})} = \frac{4}{12} = \frac{1}{3}
\]
2. **Probability of selecting a red balloon from the second package:**
\[
P(\text{red from package 2}) = \frac{4 \, (\text{red balloons})}{12 \, (\text{total balloons})} = \frac{4}{12} = \frac{1}{3}
\]
Since the selections from each package are independent events, the joint probability of both events occurring (selecting a red balloon from the first package and a red balloon from the second package) is calculated by multiplying the probabilities:
\[
P(\text{red from package 1 and red from package 2}) = P(\text{red from package 1}) \times P(\text{red from package 2}) = \frac{1}{3} \times \frac{1}{3} = \frac{1}{9}
\]
Thus, the probability that Josie will randomly select 1 red balloon from both bags is \( \frac{1}{9} \).