If A and B are two independent events with $P(A) = \frac{3}{5}$ and $P(B) =\frac{4}{9}$, then P(A' ∩ B') is equal to:
Answer & explanation
Correct answer: option 4
The correct answer is OPTION 4 - $\frac{2}{9}$
$P(A)=\frac{3}{5},\;P(B)=\frac{4}{9}.$
$P(A')=1-\frac{3}{5}=\frac{2}{5}.$
$P(B')=1-\frac{4}{9}=\frac{5}{9}.$
$\text{Since }A\text{ and }B\text{ are independent, }A'\text{ and }B'\text{ are also independent.}$
$P(A'\cap B')=P(A')P(B').$
$=\frac{2}{5}\cdot\frac{5}{9}.$
$=\frac{10}{45}.$
$=\frac{2}{9}.$
$P(A'\cap B')=\frac{2}{9}.$