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, then $P\left(\overline{A}\right)+P\left(\overline{B}\right)$ is.

• A. $0.4$
• B. $0.8$
• C. $1.2$
• D. $1.4$

Answer 1

Answer: (C)

$1.2$

$P(A\cup B)=0.6$ and $P(A\cap B)=0.2$

we know that

$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$
$⟹0.6=P\left(A\right)+P\left(B\right)-0.2$
$⟹P\left(A\right)+P\left(B\right)=0.8$

$⟹1-P\left(\overline{A}\right)+1-P\left(\overline{B}\right)=0.8$
$⟹-\left[P\right(\overline{A})+P(\overline{B}\left)\right]=0.8-2$

$⟹P\left(\overline{A}\right)+P\left(\overline{B}\right)=1.2$

Hence, option C is correct.