Question

If $A$ and $B$ are two mutually exclusive events, then $P(A+B)=$

• A. $P\left(A\right)+P\left(B\right)–P\left(AB\right)$
• B. $P\left(A\right)–P\left(B\right)$
• C. $P\left(A\right)+P\left(B\right)$
• D. $P\left(A\right)+P\left(B\right)+P\left(AB\right)$

Answer 1

The correct option is C

$P\left(A\right)+P\left(B\right)$

Explanation for the correct option:

Find the value of $\mathit{P}\mathbf{(}\mathit{A}\mathbf{}\mathbf{+}\mathbf{}\mathit{B}\mathbf{)}$:

$\because$The events $A$ and $B$ are mutually exclusive,

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

As we know, $\mathit{P}\mathbf{\left(}\mathit{A}\mathit{U}\mathit{B}\mathbf{\right)}\mathbf{}\mathbf{=}\mathbf{}\mathit{P}\mathbf{\left(}\mathit{A}\mathbf{\right)}\mathbf{}\mathbf{+}\mathbf{}\mathit{P}\mathbf{\left(}\mathit{B}\mathbf{\right)}\mathbf{}\mathbf{–}\mathbf{}\mathit{P}\mathbf{(}\mathit{A}\mathbf{\cap }\mathit{B}\mathbf{)}$

$\begin{array}{rcl}\therefore P\left(AUB\right)& =& P\left(A\right)+P\left(B\right)–0\\ & =& P\left(A\right)+P\left(B\right)\end{array}$

Hence, Option ‘C’ is Correct.