Question

The probability that at least one of the two events $A$ and $B$ occurs is $0.6$. If $A$ and $B$ occur simultaneously with probability $0.3$, then $P\left(\overline{A}\right)+P\left(\overline{B}\right)$ is
$\left(a\right)1.2\left(b\right)1.1\left(c\right)1.0\left(d\right)0.9$

Answer 1

Given $P(A\cup B)=0.6$ and $P(A\cap B)=0.3$

We know that,
$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$
$\Rightarrow 0.6=(1-P(\overline{A}\left)\right)+(1-P(\overline{B}\left)\right)-0.3$
$\Rightarrow P\left(\overline{A}\right)+P\left(\overline{B}\right)=1.1$

Answer: $\left(b\right)$