We applied a fast probabilistic inversion technique based on neural networks to predict 3D petrophysical properties from inverted pre-stack seismic data. The objective of petrophysical inversion is to estimate the joint probability density function (PDF) of model vectors consisting of porosity, clay content, and water saturation components at each point in the reservoir, from data vectors consisting of compressional- and shear-wave-impedance components; obtained from the inversion of AVO seismic data. The petrophysical inverse problem is significantly non-linear, and due to the large number of data points in a seismic cube we need to apply fast inversion methods. In this study we consider the effect of different sources of uncertainty on the a posteriori PDF of model parameters. These sources include variations in effective pressure, bulk modulus and density of hydrocarbon, random noise in recorded data, and uncertainties in petrophysical forward function. Results show that the standard deviations of all model parameters are reduced after inversion, which shows that the inversion process provides information about all parameters. The reduction of uncertainty in water saturation is smaller than that for porosity and clay content; nevertheless the maximum of the a posteriori PDF of water saturation (MAP) clearly shows the boundary between brine saturated and oil saturated rocks.