Question
If $$C$$ and $$D$$ are two events such that $$C \subset D$$ and $$P\left( D \right) \ne 0,$$ then the correct statement among the following is
A.
$$P\left( {\frac{C}{D}} \right) \geqslant P\left( C \right)$$
B.
$$P\left( {\frac{C}{D}} \right) < P\left( C \right)$$
C.
$$P\left( {\frac{C}{D}} \right) = \frac{{P\left( D \right)}}{{P\left( C \right)}}$$
D.
$$P\left( {\frac{C}{D}} \right) = P\left( C \right)$$
Answer :
$$P\left( {\frac{C}{D}} \right) \geqslant P\left( C \right)$$
Solution :
In this case, $$P\left( {\frac{C}{D}} \right) = \frac{{P\left( {C \cap D} \right)}}{{P\left( D \right)}} = \frac{{P\left( C \right)}}{{P\left( D \right)}}$$
Where, $$0 \leqslant P\left( D \right) \leqslant 1,$$ : hence $$P\left( {\frac{C}{D}} \right) \geqslant P\left( C \right)$$