Question

If $P(A\cup B)=0.8,P(A\cap B)=0.3$, 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 $0.9$

$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$
$P(A\cup B)=1-P\left(\overline{A}\right)+1-P\left(\overline{B}\right)-P(A\cap B)$
$0.8=1-P\left(\overline{A}\right)+1-P\left(\overline{B}\right)-0.3$
$P\left(\overline{A}\right)+P\left(\overline{B}\right)=2-0.8-0.3=0.9$