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Let's solve the problem step by step:

We are given:
- 4 green marbles
- 6 red marbles
- 5 blue marbles

### Step 1: Total marbles in the bag
The total number of marbles is:
\[
4 + 6 + 5 = 15
\]

### Step 2: First event (drawing a green marble)
The probability of drawing a green marble first is the ratio of green marbles to the total marbles:
\[
P(\text{Green first}) = \frac{4}{15}
\]

### Step 3: Second event (drawing a blue marble)
Since the marble is replaced after checking its color, the total number of marbles remains the same (15 marbles). Therefore, the probability of drawing a blue marble next is:
\[
P(\text{Blue second}) = \frac{5}{15} = \frac{1}{3}
\]

### Step 4: Combine the probabilities
To find the total probability of the first marble being green and the second being blue (with replacement), we multiply the probabilities of these independent events:
\[
P(\text{Green first and Blue second}) = P(\text{Green first}) \times P(\text{Blue second}) = \frac{4}{15} \times \frac{1}{3} = \frac{4}{45}
\]

Thus, the probability that the first marble is green and the second is blue is:
\[
\boxed{\frac{4}{45}} \quad \text{(Option A)}
\]

Would you like a more detailed explanation or have any questions?

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Here are 5 related questions to expand your understanding:
1. What is the probability of drawing two green marbles in a row with replacement?
2. How would the probability change if the marbles were not replaced?
3. What is the probability of drawing a red marble followed by a blue marble?
4. If a third marble is drawn (with replacement), what is the probability that it will be red?
5. How does the concept of independent events apply to this problem?

**Tip:** For problems with replacement, remember that the total number of objects (like marbles) remains constant after each draw.

A bag contains 4 green marbles, 6 red marbles, and 5 blue marbles. One marble is taken from the bag and put back after checking its color. A second marble is then taken out. What is the probability that the first is green and the second blue?

Learn how to calculate the probability of drawing a green marble followed by a blue marble from a bag containing 4 green, 6 red, and 5 blue marbles with replacement. This problem demonstrates independent events in probability. Suitable for Grades 7-9.

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