Question

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

• A. $0.4$
• B. $0.8$
• C. $1.2$
• D. $1.6$

Answer 1

Answer: (C)

$1.2$

$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$
$P(A\cup B)=1-P\left(\overline{A}\right)+1-P\left(\overline{B}\right)-P(A\cap B)$
$0.6=2-P\left(\overline{A}\right)-P\left(\overline{B}\right)-0.2$ Given: $[P(A\cup B)=0.6;P(A\cap B)=0.2]$
$P\left(\overline{A}\right)+P\left(\overline{B}\right)=2-0.6-0.2=1.2$