Question

If P(B')=0.65, $P(A\cup B)=0.85$ and A and B are independent events, then find P(A).

Answer 1

$P\left(B^{{}^{\prime }}\right)=0.65\Rightarrow 1-P\left(B\right)=0.65\Rightarrow P\left(B\right)=0.35$

$A$ and $B$ are independent .

$\therefore P(A\cup B)=P\left(A\right)+P\left(B\right)=0.85\Rightarrow P\left(A\right)+0.35=0.85\Rightarrow P\left(A\right)=0.85-0.35\Rightarrow P\left(A\right)=0.50$