Cumulative oil predictions are made from stochastically inverted earth attributes. The inverted attributes are from the SEAM Life of Field model and an offshore field in West Africa. To perform the prediction, we use a naïve Bayesian classifier for its transparency in methodology, computational efficiency and flexibility. The inverted properties we use for classification consist of porosity, P-S wave velocity ratio (Vp/Vs), acoustic impedance and density which are extracted from within a set radius around the well-path. The production from the wells in both SEAM and the West African field serve as the labels for the naïve Bayesian classifier, which are ultimately placed into two classes: the 'high' and 'low' producers. For calculating the accuracy of the classifier, we perform full cross-validation with a set number of training wells. The cross-validation accuracy is 78.0% and 83.3% for the SEAM model and the West African Field respectively. The classifier's sensitivity to the chosen radius around the wells and its inherent independence assumption are investigated and shown to change the bulk accuracy by less than 3.0%. We implement full reservoir classifications on SEAM to highlight potential drilling locations and show the capability of the classifier. Overall, we demonstrate how the naïve Bayesian classifier can efficiently and transparently synthesize the entire distribution of stochastic inversions of seismic data to predict oil production.