Question

If A and B are two events such that A ≠ Φ, B = Φ, then

(a) $P\left(\raisebox{1ex}{$A$}\!\left/ \!\raisebox{-1ex}{$B$}\right.\right)=\frac{P\left(A\cap B\right)}{P\left(B\right)}$ (b) $P\left(\raisebox{1ex}{$A$}\!\left/ \!\raisebox{-1ex}{$B$}\right.\right)=P\left(A\right)P\left(B\right)$
(c) $P\left(\raisebox{1ex}{$A$}\!\left/ \!\raisebox{-1ex}{$B$}\right.\right)=P\left(\raisebox{1ex}{$B$}\!\left/ \!\raisebox{-1ex}{$A$}\right.\right)=1$ (d) $P\left(\raisebox{1ex}{$A$}\!\left/ \!\raisebox{-1ex}{$B$}\right.\right)=\frac{P\left(A\right)}{P\left(B\right)}$

Answer 1

By the definition of conditional probability:
If A and B are two events such that A ≠ Φ, B = Φ, then $P\left(\raisebox{1ex}{$A$}\!\left/ \!\raisebox{-1ex}{$B$}\right.\right)=\frac{P\left(A\cap B\right)}{P\left(B\right)}$.
Hence, the correct answer is option (a).