the probability to draw:
black marble: 5/12
green: 1/12
\(black, green, black \\ \frac{5}{12} \times \frac{1 }{12 (-1) \text{ because you draw one marble)}} \times \frac{5(-1) \text{ because you draw one black marble)}}{12(-2) \text{ because you draw two marbles)}} \\ (5/12)*(1/11)*(4/10)=1/66\)
.