Answer
As given below
Work Step by Step
From the definition of Conditional Probability we have:
$P(A| B) =\frac{P(A \cap B)}{P(A)}$
when there is only $P(A) \rightarrow \frac{P(A \cap B)}{P(A)} \lt P(A)$
Multiple each side with $P(B)$ we have: $P(A \cap B) \lt P(A)P(B)$
Continue to divide both side with $P(A)$: $\frac{P(A \cap B)}{P(A)} \lt P(B)$
when $P(B|A) = \frac{P(A \cap B)}{P(A)} $
so $P(B|A) \lt P(B)$
