Question

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

• A. $0.4$
• B. $0.8$
• C. $1.2$
• D. $1.6$

Answer 1

Answer: (C)

Given, $P\left(A\cup B\right)=0.6$ and $P\left(A\cap B\right)=0.2$
$\because P\left(A\cup B\right)=P\left(A\right)+P\left(B\right)-P\left(A\cap B\right)$
$=1-P\left(\bar{A}\right)+1-P\left(\bar{B}\right)-P\left(A\cap B\right)$
$\therefore 0.6=1-P\left(\bar{A}\right)+1-P\left(\bar{B}\right)-0.2$
$\Rightarrow P\left(\bar{A}\right)+P\left(\bar{B}\right)$
$=2-0.8=1.2$