Question

Consider a jar that has 18 marbles. There are 5 red, 7 blue, and 6 green marbles. What is the probability of selecting a blue marble, replacing it, and then selecting a red marble?(1 point) Responses 0.114 0.114 0.667 0.667 0.108 0.108 0.683

Answer 1

To calculate the probability of selecting a blue marble, replacing it, and then selecting a red marble, we first find the individual probabilities of each event.

1. **Probability of selecting a blue marble**:
- There are 7 blue marbles out of a total of 18 marbles.
- Therefore, the probability of selecting a blue marble is:
\[
P(\text{Blue}) = \frac{7}{18}
\]

2. **Replacing the blue marble**:
- Since we are replacing the marble, the total number of marbles remains 18 for the next selection.

3. **Probability of selecting a red marble**:
- There are 5 red marbles out of a total of 18 marbles.
- Therefore, the probability of selecting a red marble is:
\[
P(\text{Red}) = \frac{5}{18}
\]

4. **Finding the combined probability**:
- Since these two events are independent (the first event does not affect the second because of the replacement), we multiply the probabilities:
\[
P(\text{Blue then Red}) = P(\text{Blue}) \times P(\text{Red}) = \left(\frac{7}{18}\right) \times \left(\frac{5}{18}\right)
\]
- Calculating this gives:
\[
P(\text{Blue then Red}) = \frac{7 \times 5}{18 \times 18} = \frac{35}{324}
\]

5. **Calculating the decimal approximation**:
- To find the decimal value:
\[
\frac{35}{324} \approx 0.108
\]

Therefore, the probability of selecting a blue marble, replacing it, and then selecting a red marble is approximately **0.108**.

The correct response is: **0.108**.