South African Mathematics Olympiad First Round

There are $5+6+4=15$ pens in the box, so the probability of first picking a red pen is $\frac{5}{15}=\frac{1}{3}$. This leaves $14$ pens (since the red pen is not replaced), and the probability of next picking a blue pen is $\frac{6}{14}=\frac{3}{7}$. Finally, the probability of picking a green pen is $\frac{4}{13}$. The events are not independent, and the probability is $\frac{1}{3}\times \frac{3}{7}\times \frac{4}{13}=\frac{4}{7\times 13}=\frac{4}{91}$.