JEE MAIN - Mathematics (2019 - 8th April Morning Slot - No. 4)
Let A and B be two non-null events such that
A $$ \subset $$ B . Then, which of the following statements
is always correct?
P(A|B) = 1
P(A|B) = P(B) – P(A)
P(A|B) $$ \le $$ P(A)
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)
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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