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)

$1.2$

Answer 2

The correct answer is C:1.2
Given, $P\left(A\cup B\right) = 0.6$ and $P\left(A\cap B\right) = 0.2$
we know that for A & B;
$\because P\left(A\cup B\right) = P\left(A\right) +P\left(B\right)-P\left(A\cap B\right)$
$P(A\cup{B})= 1-P\left(\bar{A}\right)+1-P\left(\bar{B}\right)-P\left(A\cap B\right)$
$\therefore 0.6 = 1-P\left(\bar{A}\right) +1 -P\left(\bar{B}\right) -0.2$
$\Rightarrow P\left(\bar{A}\right) + P\left(\bar{B}\right)$
$= 2-0.8=1.2$