Question

If $6P\left(A\right)=8P\left(B\right)=14P(A\cap B)=1$, then $P\left(A^{\prime }|B\right)=$_______

• A. $\frac{3}{7}$
• B. $\frac{4}{7}$
• C. $\frac{3}{5}$
• D. $\frac{2}{5}$

Answer 1

The correct option is A $\frac{3}{7}$

$P\left(A^{\prime }|B\right)=\frac{P(A^{\prime }\cap B)}{P\left(B\right)}$
$=\frac{P\left(B\right)-P(A\cap B)}{P\left(B\right)}=1-\frac{P(A\cap B)}{P\left(B\right)}$
$=1-\frac{\frac{1}{14}}{\frac{1}{8}}=\frac{3}{7}$