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.
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