Question

If A and B are two events such that $P(A)=\frac{1}{3},P(B)=\frac{1}{2}$ and $P(A\cap B)=\frac{1}{6}$, then P(A'|B) is

• A. $\frac{2}{3}$
• B. $\frac{1}{3}$
• C. $\frac{1}{2}$
• D. $\frac{1}{12}$

Answer 1

Answer: (A)

Given $P(A)=1/3,P(B)=1/2,P(A\cap B)=1/6$
So, $P\left(A^{\prime }|B\right)=1-P(A|B)$
$=1-\frac{P(A\cap B)}{P(B)}$
$=1-1/3$
$=2/3$