Question

If $A$ and $B$ are two mutually exclusive events, then the relation between $P\left(\overline{A}\right)$ and $P\left(B\right)$ is

• A. $P\left(B\right)\ge P\left(\overline{A}\right)$
• B. $P\left(B\right)\le P\left(\overline{A}\right)$
• C. $P\left(B\right)=P\left(\overline{A}\right)$
• D. $P\left(B\right)<P\left(\overline{A}\right)$

Answer 1

The correct option is B $P\left(B\right)\le P\left(\overline{A}\right)$

We know,
$P(A\cap B)=0$
$\because A$ and $B$ are two mutually exclusive events.
$\Rightarrow P(A\cup B)\le 1$
$\Rightarrow P\left(A\right)+P\left(B\right)\le 1$
$\Rightarrow P\left(B\right)\le P\left(\overline{A}\right)$