Question

The probability that at least one of the events $A$ and $B$ occurs is $0.7$ and they occur simultaneously with probability $\mathrm{0.2.}$ Then $P\left(\overline{A}\right)+P\left(\overline{B}\right)=$

• A. $1.8$
• B. $0.6$
• C. $1.1$
• D. $1.4$

Answer 1

The correct option is C $1.1$

We have $P(A\cup B)=0.7$ and $P(A\cap B)=0.2$.
Now, $P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$
$\Rightarrow P\left(A\right)+P\left(B\right)=0.9\Rightarrow 1-P\left(\overline{A}\right)+1-P\left(\overline{B}\right)=0.9\Rightarrow P\left(\overline{A}\right)+P\left(\overline{B}\right)=1.1$