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 equal to

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

Answer 1

Answer: (A)

$\frac{5}{7}$

Let $P\left(B\right)=b$, then we have

$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$

As $A$ and $B$ are independent events

$\therefore P(A\cup B)=P\left(A\right)+P\left(B\right)-P\left(A\right)\cdot P\left(B\right)$
$\Rightarrow 0.8=0.3+b-0.3\times b$

$\Rightarrow 0.5=0.7b$

$\Rightarrow b=\frac{5}{7}$