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Probability

Question
CBSEENMA12033629

If A and B are two events such that A ⊂ B and P(B) ≠ 0, then which of the following is correct?
  • straight P left parenthesis straight A vertical line straight B right parenthesis space equals space fraction numerator straight P left parenthesis straight B right parenthesis over denominator straight P left parenthesis straight A right parenthesis end fraction
  • straight P left parenthesis straight A vertical line straight B right parenthesis space less than thin space straight P left parenthesis straight A right parenthesis
  • straight P left parenthesis straight A vertical line straight B right parenthesis space greater or equal than space straight P left parenthesis straight A right parenthesis
  • None of these

Solution

C.

straight P left parenthesis straight A vertical line straight B right parenthesis space greater or equal than space straight P left parenthesis straight A right parenthesis

When A ⊂ B, then straight A intersection straight B space equals space straight A.
therefore space space space space straight P left parenthesis straight A vertical line straight B right parenthesis space equals space fraction numerator straight P left parenthesis straight A intersection straight B right parenthesis over denominator straight P left parenthesis straight B right parenthesis end fraction space equals fraction numerator straight P left parenthesis straight A right parenthesis over denominator straight P left parenthesis straight B right parenthesis end fraction greater or equal than straight P left parenthesis straight A right parenthesis space space space space open square brackets because space 0 space less than thin space straight P left parenthesis straight B right parenthesis space less or equal than 1 comma space space therefore space fraction numerator 1 over denominator straight P left parenthesis straight B right parenthesis end fraction greater or equal than 1 close square brackets
∴ (C) is correct answer.

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