Question
There are 100 balls in a container. 30 of them are red, 50 blue, and 20 green. We randomly select a ball, return it to the container and select another ball. What is the probability that both times balls are green?
Write your answer as a decimal.
Write your answer as a decimal.
Answers
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Answered by
GPT-4o mini
To find the probability that both times the balls selected are green, we start by identifying the probability of selecting a green ball in a single draw.
There are 20 green balls out of a total of 100 balls in the container. Thus, the probability \( P(\text{green}) \) of selecting a green ball on a single draw is:
\[
P(\text{green}) = \frac{20}{100} = 0.2
\]
Since we are drawing with replacement, the probability of selecting a green ball remains the same for each draw. Therefore, the probability of selecting two green balls consecutively is calculated as follows:
\[
P(\text{both green}) = P(\text{green}) \times P(\text{green}) = 0.2 \times 0.2
\]
Calculating the product:
\[
P(\text{both green}) = 0.2 \times 0.2 = 0.04
\]
Thus, the probability that both times the balls selected are green is:
\[
\boxed{0.04}
\]
There are 20 green balls out of a total of 100 balls in the container. Thus, the probability \( P(\text{green}) \) of selecting a green ball on a single draw is:
\[
P(\text{green}) = \frac{20}{100} = 0.2
\]
Since we are drawing with replacement, the probability of selecting a green ball remains the same for each draw. Therefore, the probability of selecting two green balls consecutively is calculated as follows:
\[
P(\text{both green}) = P(\text{green}) \times P(\text{green}) = 0.2 \times 0.2
\]
Calculating the product:
\[
P(\text{both green}) = 0.2 \times 0.2 = 0.04
\]
Thus, the probability that both times the balls selected are green is:
\[
\boxed{0.04}
\]
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