Question

Let $A$ and $B$ be two mutually exclusive events such that $P(A\cap {{B}^{c}})=0.25$ and $P({{A}^{c}}\cap B)=0.5$ . Then, $P\\{(A\cup {{B}^{c}})\\}$ is equal to

• A. $0.25$
• B. $0.50$
• C. $0.75$
• D. $0.40$

Answer 1

Answer: (A)

$0.25$

Answer 2

The correct option is(A): 0.25.

Given, $P(A\cap {{B}^{c}})=0.25$ and $P({{A}^{c}}\cap B)=0.5$
$\therefore$ $P\\{{{(A\cup B)}^{c}}\\}=1-P(A\cup B)$
$=1-\\{P(A\cap {{B}^{c}})+P({{A}^{c}}\cap B)+P(A\cap B)\\}$
$=1-(0.25+0.5+0)$
[ $\because$ A and B are mutually exclusive events
$P(A\cap B)=0$ ] $=1-0.75=0.25$