Over 50 million people worldwide suffer from epilepsy. Traditional diagnosis of epilepsy relies on tedious visual screening by highly trained clinicians from lengthy EEG recording that contains the presence of seizure (ictal) activities. Nowadays, there are many automatic systems that can recognize seizure-related EEG signals to help the diagnosis. However, it is very costly and inconvenient to obtain long-term EEG data with seizure activities, especially in areas short of medical resources. We demonstrate in this paper that we can use the interictal scalp EEG data, which is much easier to collect than the ictal data, to automatically diagnose whether a person is epileptic. In our automated EEG recognition system, we extract three classes of features from the EEG data and build Probabilistic Neural Networks (PNNs) fed with these features. We optimize the feature extraction parameters and combine these PNNs through a voting mechanism. As a result, our system achieves an impressive 94.07% accuracy.