Description: Let $U^{(n)}$ denote the maximal length arithmetic progression in a non-uniform random subset of ${0,1}^n$, where $1$ appears with probability $p_n$. By using dependency graph and Stein-Chen method, we show that $U^{(n)}-c_nln n$ converges in law to an extreme type distribution with $ln p_n=-2/c_n$. Similar result holds for $W^{(n)}$, the maximal length aperiodic arithmetic progression (mod $n$).