Question

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

• A. $\frac{5}{7}$
• B. $\frac{3}{8}$
• C. $\frac{2}{7}$
• D. $\frac{2}{9}$

Answer 1

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

Given $P\left(A\right)=0.3$, $P(A\cup B)=0.8$........(1).

Also given $A,B$ are independent then $P(A\cap B)=P\left(A\right).P\left(B\right)$......(2).

From (1) we have

$P(A\cup B)=$$P\left(A\right)+P\left(B\right)-P(A\cap B)=0.8$

$\Rightarrow P\left(A\right)+P\left(B\right)-P\left(A\right)P\left(B\right)=0.8$ [Using (2)]

$\Rightarrow P\left(B\right)-0.3P\left(B\right)=0.8-0.3$

$\Rightarrow 0.7P\left(B\right)=0.5$

$\Rightarrow P\left(B\right)=\frac{5}{7}$