jmc

If a red marble is chosen first ($\frac{12}{18}=\frac{2}{3}$ chance), then there is a $\frac{6}{17}$ chance that a blue marble will be chosen second. If a blue marble is chosen first ($\frac{6}{18}=\frac{1}{3}$ chance), then there is a $\frac{12}{17}$ chance that a red marble will be chosen second. The total probability that one red and one blue marble will be chosen is $\frac{2}{3}\cdot \frac{6}{17}+\frac{1}{3}\cdot \frac{12}{17}=\boxed{\frac{8}{17}}$.