Predrill assessment of the probability that a potential drilling spot holds hydrocarbons (HC) is of vital importance to any oil company. Of equally great value is the assessment of hydrocarbon volumes and distributions. We have developed a methodology that uses seismic data to find the probability that a vertical earth profile contains hydrocarbons and the probability distribution of hydrocarbon volumes. The method combines linearized amplitude variation with offset (AVO) inversion and stochastic rock models and predicts the joint probability distribution of the combined lithology and fluid for the entire profile. We use a Bayesian approach and find the solution of the inverse problem by Markov chain Monte Carlo simulation. The stochastic simulation benefits from a new and tailored simulation algorithm. The computational cost of finding the full joint probability distribution is relatively high and implies that the method is best suited to the investigation of a few potential drilling spots. We applied the method to a case with well control and to two locations in a prospect: one in the center and one at the outskirts. At the well location, we identify the two reservoir zones and obtain volumes that fit the log data. At the prospect, we obtain significant increases in HC probability and volume in the center, whereas there are decreases at the outskirts. Despite the large noise components in the data, the risked volumes in the center changed by a factor of three. We have designed an algorithm for computing the joint distribution of lithology, fluid, and elastic parameters for a full vertical profile. As opposed to what can be done with pointwise approaches, this allows us to calculate success probability and HC volumes.