If $P(A ∩ B) = 0.4 , P(\overline{A}∩ \overline{B})=0.3 $ then the value of $P(\overline{A})+P(\overline{B})$ is :

0.9

The correct answer is Option (4) → 0.9

$P(A ∩ B) = 0.4 , P(\overline{A}∩ \overline{B})=0.3 $

$P(\overline{\overline{A}∪ \overline{B}})=0.4$ using demorgan's law

$P(\overline{A}∪ \overline{B})=0.6$

so $P(\overline{A})+P(\overline{B})=P(\overline{A}∪ \overline{B})+P(\overline{A}∩ \overline{B})$

$=0.6+0.3=0.9$