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 $P\left(\frac{A^1}{B}\right)=$

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

Answer 1

Answer: (C)

$P\left(\frac{A^1}{B}\right)=\frac{P\left(A^1\cap B\right)}{P(B)}=\frac{P(B)-P(A\cap B)}{P(B)}$
$=\frac{\frac{1}{2}-\frac{1}{6}}{\frac{1}{2}}=\frac{2}{3}$