If $A$ and $B$ are events of a random experiment with $P(A)$ $=0.5, \mathrm{P}(\mathrm{B})=0.4$ and…
If $A$ and $B$ are events of a random experiment with $P(A)$ $=0.5, \mathrm{P}(\mathrm{B})=0.4$ and $\mathrm{P}(\mathrm{A} \cap \mathrm{B})=0.3$, then the probability that neither A nor B occurs is
$0.04$
$0.4$
$0.8$
$0.2$
Solution
We know, $P(A \cup B)=P(A)+P(B)-P(A \cap B)$
$\Rightarrow P(A \cup B)=0.5+0.4-0.3=0.6$
So probability neither A nor $B=1-0.6=0.4$