This document discusses the evaluation of network intrusion detection systems (IDS) using Markov chains and incorporates two algorithms, k-means and apriori, for classifying network activities. The study demonstrates the need for effective intrusion detection methods in light of increasing internet threats and presents experimental results showing high performance in detecting various types of attacks using the DARPA 2000 dataset. It highlights the importance of data pruning and probabilistic modeling to enhance the detection efficiency of network intrusions.