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Integrals

Question
CBSEENMA12036097

If C and D are two events such that C ⊂ D and P(D) ≠0, then the correct statement among the following is:

  • P(C|D) = P(C)

  • P(C|D)  ≥ P(C)

  • P(C|D) < P(C)

  • P(C|D) = P(D)/P(C)

Solution

B.

P(C|D)  ≥ P(C)

straight P open parentheses straight C over straight D close parentheses space equals space fraction numerator straight P space left parenthesis straight C space intersection space straight D right parenthesis over denominator straight P left parenthesis straight D right parenthesis end fraction space equals space fraction numerator straight P left parenthesis straight C right parenthesis over denominator straight P left parenthesis straight D right parenthesis end fraction
fraction numerator 1 over denominator straight P left parenthesis straight D right parenthesis space end fraction greater or equal than space 1
fraction numerator straight P left parenthesis straight C right parenthesis over denominator straight P left parenthesis straight D right parenthesis end fraction space greater or equal than space straight P left parenthesis straight C right parenthesis
straight P left parenthesis straight C right parenthesis space less or equal than space straight P space open parentheses straight C over straight D close parentheses

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