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$