The functional heterogeneity of computational Grids has highly increased due to inclusion of resources other than dedicated to Grid, like from non-dedicated desktop Grids,on-demand systems and even from P2P systems and mobile Grids. At such a diversified scale, resources exhibit different availability properties mainly due to administrators' policies for resource availability in the Grid, and their failure/unavailability properties. These make resources' availability predictions for optimized resource selection, a challenging problem. Addressing this problem, we characterize resource availability properties against their availability policies to understand their availability behavior and quantify it through availability models. We further exploit the availability/failure properties to make predictions about their availability through pattern recognition and classification. We have achieved, on average, accuracy of more than 90% and 75% in our predictions for resource instance availability and lifetime respectively.