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