Question
A basket contains 4 green marbles and 8 blue marbles. A marble is drawn without replacement. Then another marble is drawn. What is the probability that both marbles will be green?
(1 Point)
0.09
0.11
0.47
0.61
(1 Point)
0.09
0.11
0.47
0.61
Answers
GPT-4o mini
To find the probability that both marbles drawn are green, we will calculate the probability step by step.
1. **Total number of marbles**: There are \( 4 \) green marbles and \( 8 \) blue marbles, so the total number of marbles is:
\[
4 + 8 = 12
\]
2. **Probability of drawing the first green marble**: The probability of drawing a green marble first is:
\[
\frac{\text{Number of green marbles}}{\text{Total number of marbles}} = \frac{4}{12} = \frac{1}{3}
\]
3. **Probability of drawing the second green marble**: After drawing the first green marble, there are now \( 3 \) green marbles left and a total of \( 11 \) marbles. So, the probability of drawing a second green marble is:
\[
\frac{3}{11}
\]
4. **Combined probability**: To find the probability of both events happening (drawing two green marbles), we multiply the probabilities of each individual event:
\[
P(\text{both green}) = P(\text{first green}) \times P(\text{second green}) = \frac{1}{3} \times \frac{3}{11} = \frac{3}{33} = \frac{1}{11}
\]
Now, to convert \(\frac{1}{11}\) into a decimal approximate form:
\[
\frac{1}{11} \approx 0.0909
\]
The closest answer choice given is:
**0.09**
Therefore, the probability that both marbles drawn will be green is **0.09**.
1. **Total number of marbles**: There are \( 4 \) green marbles and \( 8 \) blue marbles, so the total number of marbles is:
\[
4 + 8 = 12
\]
2. **Probability of drawing the first green marble**: The probability of drawing a green marble first is:
\[
\frac{\text{Number of green marbles}}{\text{Total number of marbles}} = \frac{4}{12} = \frac{1}{3}
\]
3. **Probability of drawing the second green marble**: After drawing the first green marble, there are now \( 3 \) green marbles left and a total of \( 11 \) marbles. So, the probability of drawing a second green marble is:
\[
\frac{3}{11}
\]
4. **Combined probability**: To find the probability of both events happening (drawing two green marbles), we multiply the probabilities of each individual event:
\[
P(\text{both green}) = P(\text{first green}) \times P(\text{second green}) = \frac{1}{3} \times \frac{3}{11} = \frac{3}{33} = \frac{1}{11}
\]
Now, to convert \(\frac{1}{11}\) into a decimal approximate form:
\[
\frac{1}{11} \approx 0.0909
\]
The closest answer choice given is:
**0.09**
Therefore, the probability that both marbles drawn will be green is **0.09**.