Correct. The number of ways to choose 2 of the 5 purple balls is $\displaystyle\frac{{{5}}}{{{23}}}={10}\usepackage{cmbright}\Huge\$ and the number of ways to choose 2 of the 30 balls is $\displaystyle\frac{{{30}}}{{{228}}}={435}\usepackage{cmbright}\Huge\$ , so the probability that both balls are purple is $\displaystyle\frac{{10}}{{435}}=\frac{{2}}{{87}}\usepackage{cmbright}\Huge\$ .