Question

$A$ and $B$ are two independent events of an experiment .if $P\left(notB\right)=0.65,P\left(A\cup B\right)=0.85$ ,find $P\left(A\right)$.

Answer 1

$P\left(\overline{B}\right)=0.65$

$\Rightarrow P\left(\overline{B}\right)=1-P\left(B\right)=0.65$

$\Rightarrow P\left(B\right)=0.35$,$P(A\cup B)=0.85$

now, $P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$ since $A,B$ are independent events.

$\Rightarrow 0.85=P\left(A\right)+0.35-P\left(A\right)\left(0.35\right)$

$\therefore 0.50=0.65P\left(A\right)$

$\Rightarrow P\left(A\right)=\frac{0.50}{0.65}=\frac{10}{13}$