Question

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

• A. $0.8$
• B. $1.2$
• C. $1.4$
• D. $0.9$

Answer 1

The correct option is B $1.2$

It is given that $P(A\cup B)=0.6\text{and}P(A\cap B)=0.2$
$\Rightarrow P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$
$\Rightarrow 0.6=P\left(A\right)+P\left(B\right)-0.2$
$\Rightarrow 0.8=1-P\left(\overline{A}\right)+1-P\left(\overline{B}\right)$
$\Rightarrow P\left(\overline{A}\right)+P\left(\overline{B}\right)=1.2$