Question

If $A$ and $B$ are two events of a sample space $S$ such that $P\left(A\right)=0.2,P\left(B\right)=0.6$ and $P\left(A|B\right)=0.5$ then $P\left(A^{\prime }|B\right)=$

• A. $\frac{1}{2}$
• B. $\frac{3}{10}$
• C. $\frac{1}{3}$
• D. $\frac{2}{3}$

Answer 1

The correct option is A $\frac{1}{2}$

$P\left(A|B\right)=0.5\Rightarrow \frac{P(A\cap B)}{P\left(B\right)}=0.5$
$P(A\cap B)=0.5\left(P\right(B\left)\right)=\left(0.5\right)\left(0.6\right)=0.3$
$P\left(A^{\prime }|B\right)=\frac{P(A^{\prime }\cap B)}{P\left(B\right)}=\frac{P\left(B\right)-P(A\cap B)}{P\left(B\right)}=\frac{0.6-0.3}{0.6}=\frac{0.3}{0.6}=\frac{1}{2}$