Let's find the probability that Aakesh will select a green marble from each of the two bags. Here are the steps to solve this problem:
1. Determine the total number of marbles in the first bag:
- The first bag contains 6 red marbles, 4 blue marbles, and 5 green marbles.
- Total number of marbles in the first bag = 6 + 4 + 5 = 15.
2. Find the probability of selecting a green marble from the first bag:
- Number of green marbles in the first bag = 5.
- Probability of selecting a green marble from the first bag = [tex]\(\frac{\text{Number of green marbles in the first bag}}{\text{Total number of marbles in the first bag}}\)[/tex].
- Probability = [tex]\(\frac{5}{15} = \frac{1}{3}\)[/tex].
3. Determine the total number of marbles in the second bag:
- The second bag contains 3 red marbles, 1 blue marble, and 5 green marbles.
- Total number of marbles in the second bag = 3 + 1 + 5 = 9.
4. Find the probability of selecting a green marble from the second bag:
- Number of green marbles in the second bag = 5.
- Probability of selecting a green marble from the second bag = [tex]\(\frac{\text{Number of green marbles in the second bag}}{\text{Total number of marbles in the second bag}}\)[/tex].
- Probability = [tex]\(\frac{5}{9}\)[/tex].
5. Calculate the total probability of selecting a green marble from both bags:
- The total probability is the product of the individual probabilities from each bag.
- Total probability = [tex]\(\left(\frac{1}{3}\right) \times \left(\frac{5}{9}\right) = \frac{1 \cdot 5}{3 \cdot 9} = \frac{5}{27}\)[/tex].
Hence, the probability that Aakesh will select a green marble from each bag is [tex]\(\frac{5}{27}\)[/tex].
Therefore, the correct answer is:
C. [tex]\(\frac{5}{27}\)[/tex].
