I was asked to verify if is this is true or false.
$$P(AB)\leq P(A)P(B)$$
I tried to find a counterexample to proof is false, but every thing I try says that the intersection is less than or equal to the product.
2026-04-28 09:39:48.1777369188
Probability inequality with intersection true /
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Any example where $A \subseteq B$ is a good counterexample.
In fact
$$P(AB)=P(A)\geq P(A)P(B)$$
as $P(B)\leq 1$