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. $3/7$
• B. $4/7$
• C. $5/7$
• D. $6/7$

Answer 1

The correct option is C $5/7$

We have,
$0.8=P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$
$=P\left(A\right)+P\left(B\right)-P\left(A\right)P\left(B\right)$
$[\because$ $A$ and $B$ are independent]
$=0.3+P\left(B\right)-\left(0.3\right)P\left(B\right)$
$\Rightarrow 0.5=\left(0.7\right)P\left(B\right)\Rightarrow P\left(B\right)=5/7$.