Question :
If C and D are two events such that C \(\subset\) D and P(D) \(\ne\) 0, then the correct statement among the following is
(a) P(C/D) \(\ge\) P(C)
(b) P(C/D) < P(C)
(c) P(C/D) = \(P(D)\over P(C)\)
(d) P(C/D) = P(C)
Solution :
As P(C/D) = \(P(C \cap D)\over P(D)\)
= \(P(C)\over P(D)\) …….(i) [ \(\because\) C \(\subset\) D]
Also, as P(D) \(\le\) 1
\(\therefore\) \(1\over P(D)\) \(\ge\) 1
and \(P(C)\over P(D)\) \(\ge\) P(C) …..(ii)
P(C/D) \(\ge\) P(C)
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