GMAT Quantitative Reasoning Practice Test 3

The probability for the first one to be black is: $\frac{4}{\left(4+6\right)}=\frac{2}{5}$.
The probability for the second one to be black is: $\frac{3}{\left(3+6\right)}=\frac{1}{3}$.
The probability for the third one to be black is: $\frac{2}{\left(2+6\right)}=\frac{1}{4}$.
The probability for all three events is $\left(\frac{2}{5}\right)\times \left(\frac{1}{3}\right)\times \left(\frac{1}{4}\right)=\frac{1}{30}$.