Question

If events $A$ and $B$ are independent and $P\left(A\right)=0.15,P(A\cup B)=0.45$, then $P\left(B\right)=$

• A. $\frac{6}{13}$
• B. $\frac{6}{17}$
• C. $\frac{6}{19}$
• D. $\frac{6}{23}$

Answer 1

Answer: (B)

$\frac{6}{17}$

Given, $P\left(A\right)=0.15$, $P(A\cup B)$ = 0.45
We have $P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$
and $P(A\cap B)=P\left(A\right).P\left(B\right)$
Therefore, $0.45=0.15+P\left(B\right)-0.15P\left(B\right)$
$\Rightarrow 0.30=0.85P\left(B\right)$
$\Rightarrow P\left(B\right)=$ $\frac{30}{85}$ $=$ $\frac{6}{17}$