Question

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

• A. $P(A)<P(\bar{B})$
• B. $P(A)>P(\bar{B})$
• C. $P(A)<P(B)$
• D. none of these

Answer 1

Answer: (A)

$\because A$ and $B$ are two mutually exclusive events
$\therefore A\cap B=\varphi \Rightarrow A\subseteq \bar{B}$ and $B\subseteq \wedge$
$\Rightarrow P(\Lambda )\le P(\bar{B})$ and $P(B)\le P(\bar{\Lambda })$
Note : Two events $A$ and $B$ are said to be mutually exclusive events if $A\cap B=\varphi$.