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The probability of pulling a green marble on the first draw is 5/19. Since we do not replace the marbles, the probability of pulling a green marble on the second draw is now 4/18 (since there are now 4 green marbles left out of a total of 18 marbles). Finally, the probability of pulling a green marble on the third draw is 3/17.
To find the probability that all three marbles are green, we multiply the probabilities of each draw together:
(5/19) * (4/18) * (3/17) = 60/5815
So the probability that all three marbles are green is 60/5815.