A simple model for the inclusion of precursors in the estimation of core-melt probability is described. The probability of a core melt is divided into the product of a probability for the occurrence of a precursor and a probability of failure of the remainder of the system. The Rasmussen estimates (suitably simplified) are used as a prior distribution, and the Bayesian algorithm is used to add the information about the number of precursors observed and the absence (so far) of a core melt. The resulting decrease in the current estimate of core-melt probability is then calculated and is, for reasonable choices of parameter, a factor of 2 to 4. The model is meant to be illustrative.