We have described two statistical models based on Binomial mixture models to infer SNVs from aligned NGS data obtained from tumors. We demonstrated that a probabilistic approach to modeling allelic counts obviates the need for depth-based thresholding of the data, and how fitting the model to real data to estimate parameters is superior to Maq, which uses fixed parameter settings on the assumption that the data come from a normal human genome. In addition, we extended the basic Binomial mixture to model mapping and base qualities by using a probabilistic weighting technique. This eliminates the need to employ arbitrary thresholds on base and mapping qualities and instead lets the model determine the strength of contribution of each read to the inference of the genotype. Finally, we showed that even further gains in accuracy can be obtained by combining moderate thresholding and probabilistic weighting of the base and mapping qualities. Importantly, gains in accuracy by the SNVMix models were shown in both transcriptome and genome data.