8. Let $n$ be a positive integer, and randomly select non-empty subsets $A$ and $B$ of $\{1,2, \cdots, n\}$. Then the probability that $A \cap B$ is not an empty set is
The number of ways to choose non-empty subsets $A$ and $B$ is $\left(2^{n}-1\right)^{2}$. When $A \cap B$ is not an empty set, the number of ways to choose $A, B$ is $4^{n}-3^{n}$. Let $E=$ “$A \bigcap B$ is not an empty set”, so $P(E)=\frac{4^{n}-3^{n}}{\left(2^{n}-1\right)^{2}}$.