Question

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

• A. $\frac{1}{5}$
• B. $\frac{1}{2}$
• C. $\frac{1}{3}$
• D. $\frac{1}{4}$

Answer 1

The correct option is A $\frac{1}{5}$

Given : $P\left(A\right)=0.5$ and $P\left(B\right)=0.3$
$\therefore P(\overline{A}\cap \overline{B})=1-P(A\cup B)$
$=1-\left(P\right(A)+P(B\left)\right)=1-(0.5+0.3)=0.2$
$(\because (A\cap B)=\varphi )$