Final answer:
The exact probability of drawing all three green marbles is 35/816 or approximately 4.29%.
Step-by-step explanation:
To find the probability of drawing all three green marbles, we need to determine the total number of possible outcomes and the number of favorable outcomes.
The total number of possible outcomes is the number of ways three marbles can be drawn from a bag of 18 marbles (6 red + 5 blue + 7 green).
This can be calculated using combinations: 18C3 = 816.
The number of favorable outcomes is the number of ways three green marbles can be drawn from the bag (7 green marbles).
This can be calculated using combinations: 7C3 = 35.
Therefore, the exact probability of drawing all three green marbles is 35/816 = 0.0429 (rounded to four decimal places) or approximately 4.29%.