If A and B are two independent events with $P(A) = \frac{3}{5}$ and $P(B) = \frac{4}{9}$, then $P\left( {{A^\prime } \cap {B^\prime }} \right)$ equals to

$P\left( {{A^\prime } \cap {B^\prime }} \right) = 1 - P(A \cup B)$

$= 1 - [P(A) + P(B) - P(A \cap B)]$

$= 1 - \left[ {\frac{3}{5} + \frac{4}{9} - \frac{3}{5} \times \frac{4}{9}} \right]$

$= 1 - \left[ {\frac{{27 + 20 - 12}}{{45}}} \right] = 1 - \frac{{35}}{{45}} = \frac{{10}}{{45}} = \frac{2}{9}$