Question

If A & B are independent events such that $P\left(B\right)=\frac{2}{7},P(A\cup \overline{B})=0.8$, then $P\left(A\right)$ is equal to

• A. $0.1$
• B. $0.2$
• C. $0.3$
• D. $0.4$

Answer 1

The correct option is C $0.3$

$P(A\cup \overline{B})=0.8$
$P\left(B\right)=\frac{2}{7}$
$\Rightarrow P\left(A\right)+P\left(\overline{B}\right)-P(A\cap \overline{B})=0.8$ & $P\left(\overline{B}\right)=1-\frac{2}{7}$
$\Rightarrow P\left(A\right)+P\left(\overline{B}\right)-P\left(A\right)P\left(\overline{B}\right)=0.8$ & $P\left(\overline{B}\right)=\frac{5}{7}$

$\Rightarrow P\left(A\right)+\frac{5}{7}-\frac{5}{7}P\left(A\right)=0.8\Rightarrow \frac{2}{7}P\left(A\right)=\frac{3}{35}$

$\Rightarrow P\left(A\right)=0.3$