If $C$ and $D$ are two events such that $C \subset D$ and $P(D) \neq 0$, then the correct statement among…
If $C$ and $D$ are two events such that $C \subset D$ and $P(D) \neq 0$, then the correct statement among the following is
-
$P(C \mid D) \geq P(C)$
-
$P(C \mid D) < P(C)$
-
$P(C \mid D)=\frac{P(D)}{P(C)}$
-
$P(C \mid D)=P(C)$
Solution
$\mathrm{C} \cap \mathrm{D}=\mathrm{C} \Rightarrow \mathrm{P}(\mathrm{C} \cap \mathrm{D})=\mathrm{P}(\mathrm{C}) \Rightarrow \mathrm{P}\left(\frac{\mathrm{C}}{\mathrm{D}}\right)=\frac{\mathrm{P}(\mathrm{C} \cap \mathrm{D})}{\mathrm{P}(\mathrm{D})} \geq \mathrm{P}(\mathrm{C})$
Asked in: JEE Main 2011
Practice more Probability questions on Aicharya