Two events $A$ and $B$ will be independent, then

$P(\overline A ∩\overline B)= [1-P(A)][1-P(B)]$

The correct answer is Option (1) → $P(\overline A ∩\overline B)= [1-P(A)][1-P(B)]$

Correct condition when events $A$ and $B$ are independent is:

${P(\overline{A} \cap \overline{B}) = [1 - P(A)] \cdot [1 - P(B)]}$

For independent events, we know:

$P(A \cap B) = P(A) \cdot P(B)$

Using De Morgan's law:

$\overline{A} \cap \overline{B} = \overline{A \cup B}$

But for independent events:

$P(\overline{A} \cap \overline{B}) = P(\overline{A}) \cdot P(\overline{B}) = (1 - P(A))(1 - P(B))$