The probability of event $A$occurring is$0.5$ and $B$occurring is $0.3$. If $A$ and $B$ are mutually exclusive events, then the 

probability of neither  $A$ and $B$ occurring is 

We have, 

$P\left(A\right)=0.5, P\left(B\right)=0.3$

Required probability = $P(\overline{A}\cap \overline{B} )=P\overline{(A\cup B)}$

        $=1-P(A\cup B)$

    $=1-\left\{P\right(A)+P(B\left)\right\}$                                  $\left[\begin{array}{l}\because A,B\text{ are mutually }\\ \text{ exclusive events }\end{array}\right]$

    $=1-(0.5+0.3)=0.2$