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Ad hoc wireless network with black hole attacks, denial of service attacks and malicious attacks are investigated to study if we can detect harmful activities in a timely manner. A popular simulator NS2 was used to create a controlled wireless network environment. The network was built with 33 nodes with AODV protocol and traffic data was collected from the network. The probability based Naïve Bayesian classifier was used with 10 attributed derived from the traffic data. The classification rates obtained is over 97% when numeric attribute values are discretized in Naïve Bayesian classifier. It is observed that in our network simulation, denial-of-service attacks and black hole attacks are always correctly detected while malicious attacks and normal traffic are not.