Question

The probability that at least one of the events $A$ and $B$ occur is $0.6$. If $A$ and $B$ occurs simultaneously with probability $0.2$, then $P\left(\overline{A}\right)+P\left(\overline{B}\right)$ is

• A. $0.4$
• B. $0.8$
• C. $1.2$
• D. $1.4$
• E. None of these

Answer 1

The correct option is C $1.2$

Given, $P(A\cup B)=0.6,P(A\cap B)=0.2$
$\therefore P\left(\overline{A}\right)+P\left(\overline{B}\right)=(1-P\left(A\right))+(1-P\left(B\right))=2-(P\left(A\right)+P\left(B\right))=2-(P(A\cup B)+P(A\cap B))=2-(0.6+0.2)=1.2$