Solution:
Answer: (B) $P\left(A^{\prime} B^{\prime}\right)=[1-P(A)][1-P(B)]$
Concept: Two events are independent, statistically independent, or stochastically independent if the occurrence of one does not affect the probability of occurrence of the other.
Explanation:
$P\left(A^{\prime} B^{\prime}\right)=[1-P(A)][1-P(B)]$
$$
\Rightarrow P\left(A^{\prime} \cap B^{\prime}\right)=1-P(A)-P(B)+P(A) P(B)
$$
$$
\Rightarrow 1-P(A \cup B)=1-P(A)-P(B)+P(A) P(B)
$$
$=-[P(A)+P(B)-P(A \cap B)]=-P(A)-P(B)+P(A) P(B)$
$=-P(A)-P(B)+P(A \cap B)=-P(A)-P(B)+P(A) P(B)$
$\Rightarrow P(A \cap B)=P(A) \cdot P(B)$
Final Answer: Hence, it shows $A$ and $B$ are Independent events.