Question

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

• A. $\frac{5}{7}$
• B. $\frac{2}{3}$
• C. $1$
• D. None of these

Answer 1

Answer: (A)

$\frac{5}{7}$

Since $A$ and $B$ are independent events.
$\therefore$ $P(A\cup B)=P\left(A\right)+P\left(B\right)-P\left(A\right).P\left(B\right)$
$\Rightarrow 0.8=0.3+P\left(B\right)-0.3P\left(B\right)$
$\Rightarrow$ $0.5=P\left(B\right)(1-0.3)$
$\Rightarrow \frac{0.5}{0.7}=P\left(B\right)$
$\Rightarrow$ $P\left(B\right)=\frac{5}{7}$