Question

Given $P\left(A\right)=0.5,P\left(B\right)=0.4,P(A\cap B)=0.3,$ then $P\left(A^{\prime }/B^{\prime }\right)$ is equal to

• A. $1/3$
• B. $1/2$
• C. $2/3$
• D. $3/4$

Answer 1

The correct option is C $2/3$

$P\left(A^{\prime }|B^{\prime }\right)=\frac{P(A^{\prime }\cap B^{\prime })}{P\left(B^{\prime }\right)}$
$=\frac{P(A\cup B{)}^{\prime }}{P\left(B^{\prime }\right)}$
$=\frac{1-P(A\cup B)}{1-P\left(B\right)}$
$=\frac{1-\left[P\right(A)+P(B)-P(A\cap B\left)\right]}{1-P\left(B\right)}$
$=\frac{1-[0.5+0.4-0.3]}{1-0.4}$
$=\frac{0.4}{0.6}$
$=\frac{2}{3}$