Step 1 :There are 4 red marbles, 3 blue marbles, and 7 green marbles in the bag.
Step 2 :The total number of marbles in the bag is 4 (red) + 3 (blue) + 7 (green) = 14 marbles.
Step 3 :The probability of an event is calculated by dividing the number of favorable outcomes by the total number of outcomes.
Step 4 :In this case, the favorable outcome is selecting a blue marble, and the total number of outcomes is the total number of marbles in the bag.
Step 5 :So, the probability of selecting a blue marble is \(\frac{3}{14}\).
Step 6 :Final Answer: \(\boxed{C. \frac{3}{14}}\)