# 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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