There are 5+3+2=10 marbles in the bag, 5 of which are green, so the probability of the first marble being green is 5/10=½.
That leaves 9 marbles in the bag (because the green is not replaced), 4 of which are green, so the probability of the second marble being green is 4/9, and there are 8 remaining marbles, 3 of which are green.
The probability of the third marble being green is ⅜.
Combine these probabilities: 1/2×4/9×3/8=1/12.