Let A and B be two non-null events such that A $$ \subset $$ B . Then, which of the following statements is always correct?
JEE · Math · previous-year question
- A.P(A|B) = 1
- B.P(A|B) = P(B) – P(A)
- C.P(A|B) $$ \le $$ P(A)
- D.P(A|B) $$ \ge $$ P(A)correct
Answer
D. P(A|B) $$ \ge $$ P(A)
Explanation
$$P\left( {{A \over B}} \right) = {{P\left( {A \cap B} \right)} \over {P\left( B \right)}}$$ As A $$ \subset $$ B, then P(A$$ \cap $$B) = P(A) $$ \therefore $$ $$P\left( {{A \over B}} \right) = {{P\left( A \right)} \over {P\left( B \right)}}$$ As P(B) $$ \le $$ 1 $$ \therefore $$ $${{P\left( A \right)} \over {P\left( B \right)}}$$ $$ \ge $$ P(A)
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