Question

If $\mathbf{C}$ and $\mathit{D}$ are two events such that $\mathit{C}\mathbf{\subset }\mathit{D}$, and$\mathit{P}\mathbf{\left(}\mathit{D}\mathbf{\right)}\mathbf{\ne }\mathbf{0}$, then the correct statement among the following is

• A. $\mathit{P}\mathbf{\left(}\mathit{C}\mathbf{\right|}\mathit{D}\mathbf{)}\mathbf{=}\mathbf{}\mathit{P}\mathbf{(}\mathit{C}\mathbf{)}$
• B. $\mathit{P}\mathbf{\left(}\mathit{C}\mathbf{\right|}\mathit{D}\mathbf{)}\mathbf{\ge }\mathbf{}\mathit{P}\mathbf{(}\mathit{C}\mathbf{)}$
• C. $\mathit{P}\mathbf{\left(}\mathit{C}\mathbf{\right|}\mathit{D}\mathbf{)}\mathbf{<}\mathbf{}\mathit{P}\mathbf{(}\mathit{C}\mathbf{)}$
• D. $\mathbf{}\mathit{P}\mathbf{\left(}\mathit{C}\mathbf{\right|}\mathit{D}\mathbf{)}\mathbf{=}\mathbf{}\mathit{P}\mathbf{(}\mathit{D}\mathbf{)}\mathbf{/}\mathit{P}\mathbf{(}\mathit{C}\mathbf{)}$

Answer 1

The correct option is B

$\mathit{P}\mathbf{\left(}\mathit{C}\mathbf{\right|}\mathit{D}\mathbf{)}\mathbf{\ge }\mathbf{}\mathit{P}\mathbf{(}\mathit{C}\mathbf{)}$

Explanation for the correct option:

We know that,

$P\left(\frac{C}{D}\right)=P(\frac{C\cap D)}{P\left(D\right)}$

$=\frac{P\left(C\right)}{P\left(D\right)}$

As,

$0<P\left(D\right)\le 1$

$P\left(\frac{C}{D}\right)\ge P\left(C\right)$

Hence, correct option is (B)