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 $P\left(B\right)=...........$

• A. $5/7$
• B. $5/8$
• C. $3/4$
• D. $3/7$

Answer 1

The correct option is A $5/7$

We know $P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)=P\left(A\right)+P\left(B\right)-P\left(A\right).P\left(B\right)$ since A and B are independent.
$\Rightarrow 0.8=0.3+P\left(B\right)-0.3P\left(B\right)\Rightarrow P\left(B\right)=\frac{0.5}{0.7}=5/7$