# if the

Question:

If $\mathrm{P}(\mathrm{A})=\frac{1}{2}, \mathrm{P}(\mathrm{B})=0$, then $\mathrm{P}(\mathrm{A} \mid \mathrm{B})$ is

(A) 0 (B) $\frac{1}{2}$

(C) not defined (D) 1

Solution:

It is given that $\mathrm{P}(\mathrm{A})=\frac{1}{2}$ and $\mathrm{P}(\mathrm{B})=0$

$P(A \mid B)=\frac{P(A \cap B)}{P(B)}=\frac{P(A \cap B)}{0}$

Therefore, P (A|B) is not defined.

Thus, the correct answer is C.