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)
Responses
13
1 third
116
1 over 16
112
1 over 12
19
Responses
13
1 third
116
1 over 16
112
1 over 12
19
Answers
GPT-4o mini
To find the probability that Josie will randomly select 1 red balloon from both packages, we first calculate how many red balloons are in total and how many total balloons there are.
Since Josie bought 2 packages, and each package contains:
- 4 red balloons
- 4 green balloons
- 4 blue balloons
The total number of each color balloon in 2 packages is:
- Red balloons: \(4 + 4 = 8\)
- Green balloons: \(4 + 4 = 8\)
- Blue balloons: \(4 + 4 = 8\)
Thus, the total number of balloons:
\[
8 \text{ (red)} + 8 \text{ (green)} + 8 \text{ (blue)} = 24 \text{ total balloons}
\]
Next, we need to find the probability that Josie picks 1 red balloon from the first package and 1 red balloon from the second package.
1. The probability of selecting a red balloon from the first package:
\[
P(\text{Red from Package 1}) = \frac{4 \text{ red}}{12 \text{ total}} = \frac{1}{3}
\]
2. The probability of selecting a red balloon from the second package:
\[
P(\text{Red from Package 2}) = \frac{4 \text{ red}}{12 \text{ total}} = \frac{1}{3}
\]
Now, since the selection from each package is independent, we multiply the probabilities:
\[
P(\text{Red from both packages}) = P(\text{Red from Package 1}) \times P(\text{Red from Package 2}) = \frac{1}{3} \times \frac{1}{3} = \frac{1}{9}
\]
Thus, the probability that Josie will randomly select 1 red balloon from both packages is:
\[
\frac{1}{9}
\]
Since this is not one of the provided answers, ensure you double-check the options. However, based on the calculations, the correct solution is that the probability is \(\frac{1}{9}\).
Since Josie bought 2 packages, and each package contains:
- 4 red balloons
- 4 green balloons
- 4 blue balloons
The total number of each color balloon in 2 packages is:
- Red balloons: \(4 + 4 = 8\)
- Green balloons: \(4 + 4 = 8\)
- Blue balloons: \(4 + 4 = 8\)
Thus, the total number of balloons:
\[
8 \text{ (red)} + 8 \text{ (green)} + 8 \text{ (blue)} = 24 \text{ total balloons}
\]
Next, we need to find the probability that Josie picks 1 red balloon from the first package and 1 red balloon from the second package.
1. The probability of selecting a red balloon from the first package:
\[
P(\text{Red from Package 1}) = \frac{4 \text{ red}}{12 \text{ total}} = \frac{1}{3}
\]
2. The probability of selecting a red balloon from the second package:
\[
P(\text{Red from Package 2}) = \frac{4 \text{ red}}{12 \text{ total}} = \frac{1}{3}
\]
Now, since the selection from each package is independent, we multiply the probabilities:
\[
P(\text{Red from both packages}) = P(\text{Red from Package 1}) \times P(\text{Red from Package 2}) = \frac{1}{3} \times \frac{1}{3} = \frac{1}{9}
\]
Thus, the probability that Josie will randomly select 1 red balloon from both packages is:
\[
\frac{1}{9}
\]
Since this is not one of the provided answers, ensure you double-check the options. However, based on the calculations, the correct solution is that the probability is \(\frac{1}{9}\).