Question

If A and B are two mutually exclusive and exhaustive events, then $P\left(B\right)=1-P\left(A\right).$

• A. True
• B. False

Answer 1

The correct option is A

True

Given that, the two events are mutually exclusive and exhaustive.

Mutually exclusive $\Rightarrow P(A\cap B)=0$

Mutually Exhaustive$\Rightarrow P(A\cup B)=1$

$\Rightarrow P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)=1$

$P(A\cap B)=0)$

$\Rightarrow P\left(A\right)+P\left(B\right)=1$

$\Rightarrow P\left(B\right)=1-P\left(A\right)$
Thus, the given statement is true.