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

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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