Question

The probability of happening of an event $A$ is $0.5$ and that of $B$ is $0.3$. If $A$ and $B$ are mutually exclusive events, then find the probability of happening of neither $A$ nor $B$.

Answer 1

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

Since $A$ and $B$ are mutually exclusive, so

$P(A\cup B)=P\left(A\right)+P\left(B\right)$

Hence, required probability $=1-(0.5+0.3)=0.2$