If $A$ and $B$ are two independent events with $P(A) = \frac{3}{5}$ and $P(B) = \frac{4}{9}$, then $P(A' \cap B')$ is equal to

$\frac{2}{9}$

The correct answer is Option (4) → $\frac{2}{9}$ ##

$P(A' \cap B') = P((A \cup B)') = 1 - P(A \cup B)$

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

$= 1 - \left[ \frac{3}{5} + \frac{4}{9} - \frac{3}{5} \times \frac{4}{9} \right] \quad [∵P(A \cap B) = P(A) \cdot P(B)]$

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