Question

Let $A$ and $B$ be two events such that $P\left(A\right)=0.3$ and $P(A\cup B)=0.8$. If $A$ and $B$ are independent events, then $P\left(B\right)$ is :

• A. $\frac{2}{7}$
• B. $\frac{3}{7}$
• C. $\frac{4}{7}$
• D. $\frac{5}{7}$

Answer 1

The correct option is D $\frac{5}{7}$

$P(A\cup B)=P\left(A\right)+P\left(B\right)-P\left(A\right)P\left(B\right)$
$(\because A$ and $B$ are independent events$)$
$\Rightarrow 0.8=\left(0.3\right)+P\left(B\right)-\left(0.3\right)P\left(B\right)$
$\Rightarrow 0.5=\left(0.7\right)P\left(B\right)$
$\Rightarrow P\left(B\right)=\frac{5}{7}$