Question

If $A$ and $B$ are mutually exclusive events, then

• A. $P\left(A\right)=P(A-B)$
• B. $P\left(B\right)=P(A-B)$
• C. $P\left(A\right)=P(A\cap B)$
• D. $P\left(B\right)=P(A\cap B)$

Answer 1

The correct option is A $P\left(A\right)=P(A-B)$

Given $A$ and $B$ are mutually exclusive

$\Rightarrow P(A\cup B)=P\left(A\right)+\left(B\right)$

$\Rightarrow P(A-B)=P\left(A\right)-P\left(B\right)$

When $P\left(B\right)=0$ i.e, $P\left(A_B\right)+P\left(A\right)$
$\Rightarrow P\left(B\right)=0$ is not a sure event.

Hence, the answer is $P\left(A\right)=P(A-B).$