Question

The probability that atleast one of the events $A$ and $B$ occurs is $0.5$ . If $A$ and $B$ occur simultaneously with probability $0.2,$ then $P({{A}^{c}})+P({{B}^{c}})$ is equal to

• A. $1.0$
• B. $1.1$
• C. $0.7$
• D. $1.3$

Answer 1

Answer: (D)

$1.3$

Answer 2

Given, $P(A\cup B)=0.5$ and $P(A\cap B)=0.2$
$\therefore$ $P({{A}^{c}})+P({{B}^{c}})=1-P(A)+1-P(B)$
$=2-\\{P\,(A)+P(B)\\}$ ..(i)
$\because$ $P(A\cup B)=P(A)+P(B)-P(A\cap B)$
$\therefore$ $0.5=P(A)+P(B)-0.2$
$\Rightarrow$ $P(A)+P(B)=0.7$
$\therefore$ From E (i), $P({{A}^{c}})+P({{B}^{c}})=2-0.7$
$=1.3$