Question

If $E$ and $F$ be events in a sample space such that $P(E\cup F)=0.8,P(E\cap F)=0.3$ and $P\left(E\right)=0.5$, then $P\left(F\right)$ is

• A. $0.6$
• B. $1$
• C. $0.8$
• D. None

Answer 1

The correct option is A $0.6$

Given, $P(E\cup F)=0.8,P(E\cup F)=0.3$ and $P\left(E\right)=0.5$
Since, $P(E\cup F)=P\left(E\right)+P\left(F\right)-P(E\cap F)$
$\Rightarrow 0.8=0.5+P\left(F\right)-0.3$
$\Rightarrow 0.8=0.2+P\left(F\right)$
$\Rightarrow P\left(F\right)=0.6$
$\therefore$ Option A is correct.