Question

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

• A. $\frac{2}{7}$
• B. $\frac{2}{3}$
• C. $\frac{3}{8}$
• D. $\frac{1}{8}$

Answer 1

Answer: (A)

$\frac{2}{7}$

Answer 2

$P\left(A \cup B'\right)=P\left(A\right)+P\left(B'\right)-P\left(A\right)P\left(B'\right)$
$\therefore\, 0.8=0.3+P\left(B'\right)-0.3P\left(B'\right)$
$\Rightarrow 0.5=P\left(B'\right)\left(0.7\right)$
$\Rightarrow P\left(B'\right)=\frac{5}{7}$
$\therefore P\left(B\right)=1-\frac{5}{7}$
$=\frac{2}{7}$