Question

If $P(A\cup B)=0.8$ and $P(A\cap B)=0.3$ then $P\left(\overline{A}\right)+P\left(\overline{B}\right)=?$

• A. $0.3$
• B. $0.5$
• C. $0.7$
• D. $0.9$

Answer 1

The correct option is D $0.9$

$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$

$\Rightarrow P\left(A\right)+P\left(B\right)=0.8+0.3=1.1$

And $P\left(\overline{A}\right)+P\left(\overline{B}\right)=1-P\left(A\right)+1-P\left(B\right)=2-1.1=0.9$