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 the probability of neither $A$ nor $B$ is

• A. $0.4$
• B. $0.5$
• C. $0.2$
• D. $0.9$

Answer 1

The correct option is C $0.2$

Probability of neither $A$ nor $B=P(A^c\cap B^c)$
$=P(A\cup B{)}^c=1-P(A\cup B)=1-P(A)-P(B\left)\right[\because P(A\cap B)=0]$
​​​​​​$=1-0.5-0.3=0.2$