JEE PYQ: Probability Question 32
Question 32 - 2019 (08 Apr Shift 1)
Let $A$ and $B$ be two non-null events such that $A \subset B$. Then, which of the following statements is always correct?
(1) $P(A|B) = P(B) - P(A)$
(2) $P(A|B) \geq P(A)$
(3) $P(A|B) \leq P(A)$
(4) $P(A|B) = 1$
Show Answer
Answer: (2)
Solution
$A \subset B \Rightarrow A \cap B = A$. $P(A|B) = \frac{P(A)}{P(B)}$. Since $P(B) \leq 1$, $P(A|B) \geq P(A)$.